Browse Matrix problems Studdy Solved!

Problem 401

Given $M$ , find $\mathrm{M}^{-1}$ and show that $\mathrm{M}^{-1} \mathrm{M}=\mathrm{I}$ . $M=\left[\begin{array}{rrr} 1 & 2 & 0 \\ 0 & 1 & 3 \\ -1 & -1 & 4 \end{array}\right]$
Find the value in the first row and first column of the product $M^{-1} M$ using matrix multiplication. Select the correct expression below and fill in the answer box to complete your selection. A. $(-3 \cdot 1)+(4 \cdot 0)+(-3 \cdot-1)=$ $\square$ (Simplify your answer.) B. $(7 \cdot 1)+(-8 \cdot 0)+(6 \cdot-1)=$ $\square$ (Simplify your answer.) C. $(7 \cdot 0)+(-8 \cdot 3)+(6 \cdot 4)=$ $\square$ (Simplify your answer.) D. $(7 \cdot 2)+(-8 \cdot 1)+(6 \cdot-1)=$ $\square$ (Simplify your answer.)

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Problem 402

Evaluate the following determinant. $\left|\begin{array}{ccc} 0 & -6 & 5 \\ -2 & 5 & -4 \\ 1 & 3 & -2 \end{array}\right|$

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Problem 403

28. Let $\mathcal{A}=\{(0,1,0),(1,2,3),(5,7,1)\}, \mathcal{B}=\{(0,1),(1,1)\}, \mathcal{C}=\{(2,1),(1,0)\}$ and let $\varphi: \mathbb{R}^{3} \rightarrow \mathbb{R}^{2}$ denote the linear mapping given by the following condition: $M(\varphi)_{\mathcal{A}}^{\mathcal{B}}=\left[\begin{array}{lll}1 & 3 & 2 \\ 2 & 4 & 3\end{array}\right]$ , Let $\psi: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ be a linear mapping given by the formula $\psi\left(\left(y_{1}, y_{2}\right)\right)=\left(y_{1}-y_{2}, y_{1}+y_{2}\right)$ . Find $M(\psi \circ \varphi)_{\mathcal{A}}^{\mathcal{C}}$ . Find a formula expressing $\psi \circ \varphi$ .

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Problem 404

30. Let $\mathcal{A}=\{(1,2,3),(2,1,0),(4,5,0)\}, \mathcal{B}=\{(2,1,2),(3,1,2),(2,1,3)\}$ . Find a matrix $C \in M_{3 \times 3}(\mathbb{R})$ , fulfilling the following condition. For a given vector $\alpha \in \mathbb{R}^{3}$ : if the coordinates of $\alpha$ in the basis $\mathcal{A}$ are $x_{1}, x_{2}, x_{3}$ and the coordinates of $\alpha$ in the basis $\mathcal{B}$ are $y_{1}, y_{2}, y_{3}$ , then $C \cdot\left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]=\left[\begin{array}{l} y_{1} \\ y_{2} \\ y_{3} \end{array}\right] .$

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Problem 405

Fast computer: Two microprocessors are compared on a sample of 6 benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are as follows: \begin{tabular}{ccccccc} \hline & \multicolumn{6}{c}{ Code } \\ \hline & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline Processor A & 28.9 & 17.1 & 21.8 & 17.6 & 20.5 & 26.4 \\ \hline Processor B & 22.4 & 18.1 & 28.9 & 28.4 & 24.7 & 27.5 \\ \hline \end{tabular} Send data to Excel
Part: $0 / 2$
Part 1 of 2 (a) Find a $98 \%$ confidence interval for the difference between the mean speeds. Let $d$ represent the speed of processor A minus the speed of processor B . Use the TI-84 Plus calculator. Round the answers to two decimal places.
A 98\% confidence interval for the difference between the mean speeds is $\square$ $<\mu_{d}<$ $\square$ .

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Problem 406

Brake wear: For a sample of 9 automobiles, the mileage (in 1000 s of miles) at which the original front brake pads were worn to $10 \%$ of their original thickness was measured, as was the mileage at which the original rear brake pads were worn to $10 \%$ of their original thickness. The results were as follows: \begin{tabular}{ccc} \hline Car & Rear & Front \\ \hline 1 & 41.6 & 32.6 \\ 2 & 35.8 & 26.7 \\ 3 & 46.4 & 37.9 \\ 4 & 46.2 & 36.9 \\ 5 & 38.8 & 29.9 \\ 6 & 51.8 & 42.3 \\ 7 & 51.2 & 42.5 \\ 8 & 44.1 & 33.9 \\ 9 & 47.3 & 36.1 \\ \hline \end{tabular} Send data to Excel
Part: $0 / 2$
Part 1 of 2 (a) Construct a $90 \%$ confidence interval for the difference in mean lifetime between the front and rear brake pads. Let $d$ represent the mileage of the rear pads minus the mileage of the front ones. Round the answers to two decimal places.
A $90 \%$ confidence interval for the mean difference in lifetime between front and rear brake pads is $\square$ $<\mu_{d}<$ $\square$ .

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Problem 407

```latex \begin{array}{l} \text{Name: Taleah Jones} \\ \text{Identify the constant of proportionality. Find your answer on the coloring grid and color the square according to the square in the problem.} \\ \begin{array}{l} B \\ E 1 \\ 18 \\ 3 \\ \hline \end{array} c \\ \begin{array}{|c|c|c|c|} \hline x & 2 & 3 & 4 \\ \hline y & 24 & 36 & 48 \\ \hline \end{array} \\ \begin{array}{|c|c|} \hline \multicolumn{2}{|l|}{\begin{array}{l} E \\ \text{Stage:} \# (x) \end{array}} \\ \hline \begin{array}{l} 2^{2} \|^{2} \sqrt[3]{n} \\ \text{Total number of sides (t)} \end{array} & \\ \hline \end{array} \\ F \\ 6 \\ \text{Sarah bought 3 pounds of grapes for \$2.25. Dan bought 4 pounds of grapes for \$3.00.} \\ \text{Pounds or Bananas:} \\ 3y = 2x \\ \begin{array}{|c|c|c|c|} \hline \begin{array}{c} \text{Hours} \\ (x) \end{array} & 3 & 6 & 9 \\ \hline \begin{array}{c} \text{Miles} \\ (y) \end{array} & 180 & 360 & 540 \\ \hline \end{array} \\ \text{red} \\ H \\ \text{light green} \end{array}

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Problem 408

wo augmented matrices for two linear systems in the variables $x, y$ , and $z$ are given The augmented matrices are in reduced row-echelon form.
For each system, choose the best description of its solution. If applicable, give the solution. (a) $\left[\begin{array}{ccc:c} 1 & 0 & -2 & 1 \\ 0 & 1 & 0 & 4 \\ 0 & 0 & 0 & -7 \end{array}\right]$ The system has no solution. The system has a unique solution. $\square$ $\square$ $\square$ $(x, y, z)=(\square, \square, \square)$ The system has infinitely many solutions. $\begin{array}{l} (x, y, z)=(x, \square, \square) \\ (x, y, z)=(\square, y, \square) \\ (x, y, z)=(\square, \square, z) \end{array}$

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Problem 409

24. Find the value of the determinant. $\left|\begin{array}{cc} 3 & -4 \\ 6 & 2 \end{array}\right|$

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Problem 410

Calculate $D(C E)$ where $C=\begin{bmatrix}3 & -7 \\ 8 & 1\end{bmatrix}$ , $D=\begin{bmatrix}9 & -2\end{bmatrix}$ , $E=\begin{bmatrix}-3 & 5 \\ -7 & 2\end{bmatrix}$ .

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Problem 411

Perform the elementary row operation $-\frac{1}{2} R_{2} \rightarrow R_{2}$ on the given matrix. $\left[\begin{array}{cc:c} 1 & 2 & 3 \\ 4 & -6 & -2 \end{array}\right]$
Resulting matrix:

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Problem 412

Perform the elementary row operation $-2 R_{1}+R_{2} \rightarrow R_{2}$ on the given matrix. $\left[\begin{array}{cc:c} 4 & 2 & 3 \\ 0 & -6 & -2 \end{array}\right]$
Resulting matrix:
$\square$

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Problem 413

$\text{Find the rank of the matrix } \begin{bmatrix} -2 & 3 & 3 \\ 3_{\mathrm{I}} & -4 & 1 \\ -5 & 7 & 2 \end{bmatrix}$

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Problem 414

Researchers thinks that two plant species depend on each other. Wherever one grows, many times ihey observe that the other plant grows there as well.
The researchers divided a big plot of land into squares of size 1 square meter and checked whether only one of the plant species were present or both or neither. The observed values are: \begin{tabular}{|l|l|l|} \hline & Species A present & Species A not present \\ \hline Species B present & 168 & 46 \\ \hline Species B not present & 32 & 51 \\ \hline \end{tabular}
The p-value of the chi-square test of independence is less than $1 \%$ . What is the correct conclusion? We have strong evidence that the two species are dependent. We have strong evidence that the two species are independent. We don't have evidence that the two species are dependent. We don't have evidence that the two species are independent.

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Problem 415

Let $A=\left[\begin{array}{lll}a & b & c \\ d & e & f \\ g & h & \mathrm{i}\end{array}\right]$ and $B=\left[\begin{array}{ccc}-8 d & 8 e & f-4 d \\ -8 a & 8 b & c-4 a \\ -8 g & 8 h & i-4 g\end{array}\right]$ .
If $\operatorname{det}(A)=-7$ , what is $\operatorname{det}(B) ?$ $\operatorname{det}(B)=$

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Problem 416

Submit test
A scientist claims that pneumonia causes weight loss in mice. The table shows the weights (in grams) of six mice before infection and two days after infection. At $\alpha=0.05$ , is there enough evidence to support the scientist's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. \begin{tabular}{|l|c|c|c|c|c|c|} \hline Mouse & $\mathbf{1}$ & $\mathbf{2}$ & $\mathbf{3}$ & $\mathbf{4}$ & $\mathbf{5}$ & $\mathbf{6}$ \\ \hline Weight (before) & 23.8 & 20.7 & 21.8 & 22.8 & 19.2 & 22.4 \\ \hline Weight (after) & 23.7 & 20.8 & 21.7 & 22.8 & 19.0 & 22.4 \\ \hline \end{tabular} (a) Identify the claim and state $\mathrm{H}_{0}$ and $\mathrm{H}_{\text {a }}$ .
What is the claim? A. Weight gain causes pneumonia in mice. B. Pneumonia causes weight loss in mice. C. Pneumonia causes weight gain in mice. D. Weight loss causes pneumonia in mice.
Let $\mu_{d}$ be the hypothesized mean of the difference in the weights (before-after). What are $\mathrm{H}_{0}$ and $\mathrm{H}_{\mathrm{a}}$ ? A. $H_{0}: \mu_{d} \neq 0$ B. $H_{0}: \mu_{d}=0$ C. $H_{0}: \mu_{d} \geq \bar{d}$ $H_{a}: \mu_{d}=0$ $H_{a}: \mu_{d} \neq 0$ $H_{a}: \mu_{d}<\bar{d}$ D. $H_{0}: \mu_{d} \geq 0$ E. $H_{0}: \mu_{d} \leq 0$ $H_{a}: \mu_{d}<0$ $H_{a}: \mu_{d}>0$ F. $H_{0}: \mu_{d} \leq \bar{d}$ $H_{a}: \mu_{d}>\bar{d}$ (b) Find the critical value(s) and identify the rejection region(s).
Select the correct choice below and fill in any answer boxes to complete your choice. (Round to three decimal places as needed.) A. $\mathrm{t}<$ $\square$ B. $t>$ $\square$

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Problem 417

6. [-/1 Points]
DETAILS MY NOTES L.ARI
Evaluate the expression. $\left(\left[\begin{array}{rrr} -2 & 0 & 1 \\ 0 & 4 & 2 \end{array}\right]-\left[\begin{array}{rrr} 4 & 1 & -5 \\ 2 & -6 & 0 \end{array}\right]\right)$ $\square$ $\square$ $\square$ $\square$ $\square$ $■$ $\Rightarrow$ II

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Problem 418

Calculate the determinant $D$ of the matrix: $\begin{bmatrix}1 & 5 & -3 & 4 \\ 1 & 3 & -2 & 1 \\ -2 & -3 & 5 & -3 \\ 3 & 5 & -3 & -2\end{bmatrix}$ .

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Problem 419

XOne or more of your values are incorrect. Remember to round to the nearest whole number.
Using the data below, fill out the table:
In a survey on social media, $56 \mathrm{U} . \mathrm{S}$ . adults selected the following toppings for their burger: \begin{tabular}{|c|c|c|c|} \hline & \begin{tabular}{c} Grilled Onions \\ Yes \end{tabular} & \begin{tabular}{c} Grilled Onions \\ No \end{tabular} & Total \\ \hline Cheese Yes & & & NaN \\ \hline Cheese No & & & NaN \\ \hline Total & NaN & NaN & NaN \\ \hline \end{tabular} Check your answer 39.3\% Cheese Only 16.1\% Grilled Onions Only
25\% Cheese AND Grilled Onions 19.6\% Neither option

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Problem 420

Fill in the blanks so that the resulting statements are true.
If $A$ is an $m \times n$ matrix and $B$ is an $n \times p$ matrix, then $A B$ is defined as an $\square$ matrix. To find the product $A B$ , the number of $\square$ in matrix A must equal the number of $\square$ in matrix $B$ .

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Problem 421

27) A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the number of units of each ingredient in each type of candy in one batch. Matrix B gives the cost of each ingredient (dollars per unit) from suppliers X and Y. What is the cost of 100 batches from supplier X?
$A = \begin{bmatrix} 4 & 6 & 1 \\ 5 & 3 & 1 \\ 3 & 3 & 1 \end{bmatrix} \begin{bmatrix} \text{cherry} \\ \text{almond} \\ \text{raisin} \end{bmatrix}$
$B = \begin{bmatrix} 3 & 2 \\ 3 & 4 \\ 2 & 2 \end{bmatrix} \begin{bmatrix} \text{sugar} \\ \text{choc} \\ \text{milk} \end{bmatrix}$
A) $\$4800$ B) $\$7800$ C) $\$3300$ D) $\$6600$

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Problem 422

Question 9
Four heirs (A, B, C, and D) must fairly divide an estate consisting of two items - a desk and a vanity - using the method of sealed bids. The players' bids (in dollars) are:
| | A | B | C | D | | :---- | :-: | :-: | :-: | :-: | | Desk | 240 | 220 | 200 | 280 | | Vanity | 220 | 200 | 100 | 120 |
The original fair share of A is worth: $\$$
In the initial allocation, player A: Select an answer and Select an answer the estate $\$$
After all is said and done, in the final allocation, player A: Select an answer and Select an answer the estate $\$$ Select an answer Gets no items Gets the desk Gets the desk and vanity Gets the vanity

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Problem 423

Let $A = \begin{bmatrix} 2 & 2 & 3 \\ 0 & -1 & -2 \\ 0 & 1 & -1 \end{bmatrix}$ . Find $\det(A + AA^{-1})$ .
6 -2 -6 7 2

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Problem 424

If $A$ is a $4 \times 4$ matrix with $\text{det } A = 2$ , find $\text{det}(\text{Adj}(A))$ .
8 -2 2 $\frac{1}{2}$ 16

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Problem 425

2): suppose a square matrix $A$ satisfies $A=2 A^{\top}$ show that $A=0$

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Problem 426

Reduce the matrix to row echelon form:
$\begin{bmatrix} 1 & -9 & 0 & -1 & 0 & -8 \\ 0 & 1 & 0 & 0 & -2 & 3 \\ 0 & 0 & 0 & 1 & 7 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}$

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Problem 427

Is it true or false that a matrix can be row reduced to multiple reduced echelon forms? Justify your answer.

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Problem 428

The matrix $C = \begin{bmatrix} 11 & 1 & 14 \\ -6 & -3 & -6 \\ -11 & -1 & -14 \end{bmatrix}$ has two distinct eigenvalues with $\lambda_1 < \lambda_2$ .
The smaller eigenvalue $\lambda_1 =$ has multiplicity and the dimension of the corresponding eigenspace is.
The larger eigenvalue $\lambda_2 =$ has multiplicity and the dimension of the corresponding eigenspace is.
Is the matrix $C$ diagonalizable? choose

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Problem 429

$A=\left(\begin{array}{rrrr} 0 & 1 & 2 & 3 \\ 1 & 1 & 1 & 1 \\ -2 & -2 & 3 & 3 \\ 1 & 2 & -2 & -3 \end{array}\right)$ (a) Use the elimination method to evaluate $\operatorname{det}(A)$ . (b) Use the value of $\operatorname{det}(A)$ to evaluate $\left|\begin{array}{rrrr} 0 & 1 & 2 & 3 \\ -2 & -2 & 3 & 3 \\ 1 & 2 & -2 & -3 \\ 1 & 1 & 1 & 1 \end{array}\right|+\left|\begin{array}{rrrr} 0 & 1 & 2 & 3 \\ 1 & 1 & 1 & 1 \\ -1 & -1 & 4 & 4 \\ 2 & 3 & -1 & -2 \end{array}\right|$

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Problem 430

Complete the sentence below. An $m$ by $n$ rectangular array of numbers is called a(n) _____.
An $m$ by $n$ rectangular array of numbers is called a(n) column index. matrix. row index. entry.

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Problem 431

Complete the sentence below. The matrix used to represent a system of linear equations is called a(n) _ matrix.
The matrix used to represent a system of linear equations is called a(n) _ matrix. coefficient augmented invertible resulting

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Problem 432

Complete the sentence below. The notation $a_{35}$ refers to the entry in the _ row and _ column of a matrix.
The notation $a_{35}$ refers to the entry in the \_\_\_\_\_ row and \_\_\_\_\_\_ column of a matrix. third fifth

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Problem 433

Determine whether the following statement is true or false.
The matrix $\begin{bmatrix} 1 & 3 & -2 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{bmatrix}$ is in row echelon form.
Choose the correct answer below. True False

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Problem 434

Role model vs. Ievel of education \begin{tabular}{lccc} & Family member & Friend or acquaintance & Stranger \\ \hline Less than high school & 0.09 & 0.12 & 0.19 \\ High school & 0.25 & 0.32 & 0.40 \\ Some college & 0.29 & 0.25 & 0.23 \\ Bachelor's degree & 0.23 & 0.19 & 0.14 \\ Advanced degree & 0.14 & 0.12 & 0.04 \\ Column total & 1.00 & 1.00 & 1.00 \end{tabular}
Based on the data, which of the following statements must be true of the people surveyed?
Choose 1 answer: (A) A person whose role model is a family member is less likely to have an advanced deffree than a person whose role model is a friend or acquaintance. (B) A person whose role model is a stranger is more likely to have high school than some college as their highest level of education. (C) A person whose highest level of education is a bachelor's degree is more likely to have a family member than a stranger as a role model. (D) A person whose highest level of education is less than high school is more likely to have a stranger than a friend or acquaintance as a role model.

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Problem 435

A report asked people who got their news from television which television sector they relied on primarily for their news: local TV, network TV, or cable TV. The results were used to generate the data in the table below. Determine whether being female is independent of choice of local TV. Explain your answer in the context of this problem. \begin{tabular}{|c|c|c|c|c|} \hline & Local TV & Network TV & Cable TV & Total \\ \hline Men & 67 & 49 & 55 & \\ \hline Women & 85 & 55 & 56 & \\ \hline Total & & & & \\ \hline \end{tabular}
Since $\square$ $=$ $\square$ \% and $\square$ $=$ $\square$ $\%$ , the events $\square$ independent. (Type integers or decimals rounded to one decimal place as needed.)

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Problem 436

Evaluate the matrix expression:
$2\begin{bmatrix} -5 & -8 \\ 6 & -7 \\ 4 & -1 \end{bmatrix} + \begin{bmatrix} -2 & -9 \\ 8 & -2 \\ 5 & 6 \end{bmatrix} - \begin{bmatrix} 5 & 5 \\ 2 & -1 \\ -9 & 0 \end{bmatrix}$
Simplify the resulting matrix.

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Problem 437

Evaluate the matrix expression:
$2\begin{pmatrix}-5 & -8 \\ 6 & -7 \\ 4 & -1\end{pmatrix} + \begin{pmatrix}-2 & -9 \\ 8 & -2 \\ 5 & 6\end{pmatrix} - \begin{pmatrix}5 & 5 \\ 2 & -1 \\ -9 & 0\end{pmatrix}$ .
Simplify the resulting matrix.

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Problem 438

Create a 3x3 magic square using the numbers 2, 5, 8, 12, 15, 18, 22, 25, and 28.

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Problem 439

Lottery machine outputs digits 0-9 in 200 trials. Find: (a) experimental probability of even numbers, (b) theoretical probability, (c) true statement about trials and probabilities. Round answers to nearest thousandths.

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Problem 440

If the price drops by \$1, how much does the total quantity demanded by Michelle, Laura, and Hillary increase? Choices: 4, 5, 2, or 3 units.

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Problem 441

Perform the indicated operation $\begin{bmatrix} 6 & -6 & 6 \\ -5 & -4 & 2 \end{bmatrix} \cdot \begin{bmatrix} 0 & -6 \\ -5 & 6 \\ 4 & 6 \end{bmatrix}$ If the operation is undefined, leave the matrix blank. This operation is defined undefined

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Problem 442

Giving a test to a group of students, the grades and gender are summarized below Grades and Gender \begin{tabular}{|c|r|r|r|r|} \hline & \multicolumn{1}{|c|}{ A } & B & C & Total \\ \hline Male & 19 & 10 & 18 & $\mathbf{4 7}$ \\ \hline Female & 2 & 3 & 9 & $\mathbf{1 4}$ \\ \hline Total & $\mathbf{2 1}$ & $\mathbf{1 3}$ & $\mathbf{2 7}$ & $\mathbf{6 1}$ \\ \hline \end{tabular}
If one student is chosen at random, find the probability that the student was female AND got a "C". Round your answer to 4 decimal places. $\square$

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Problem 443

Find B-A
$A = \begin{bmatrix} 9 & 2 \\ 9 & 1 \end{bmatrix}$ $B = \begin{bmatrix} -8 & 2 \\ 9 & -9 \end{bmatrix}$
B-A=☐

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Problem 444

d) Phuntsho factored every multiple of 4 from 4 to 40 into prime factors. He used a matrix to show how many times each prime factor (2,3,5 and 7) appeared in each number. Create Phuntsho's matrix. [2]

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Problem 445

Construct an augmented matrix for this linear system: $\begin{array}{l} x-y-4 z=5 \\ 2 x+2 z=0 \\ 4 x+y+z=3 \end{array}$ DONE

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Problem 446

Find $X_2$ (the probability distribution of the system after two observations) for the distribution vector $X_0$ and the transition matrix $T$ .
$X_0 = \begin{bmatrix} 0.25 \\ 0.60 \\ 0.15 \end{bmatrix}$ , $T = \begin{bmatrix} 0.1 & 0.1 & 0.2 \\ 0.8 & 0.7 & 0.4 \\ 0.1 & 0.2 & 0.4 \end{bmatrix}$
$X_2 = \begin{bmatrix} \phantom{0.00} \\ \phantom{0.00} \\ \phantom{0.00} \end{bmatrix}$

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Problem 447

$\begin{bmatrix} a & 1 & 0 & 1 \\ 2 & 2 & 0 & \\ 0 & 0 & 1 & 0 \\ b \end{bmatrix}$
Perform Gaussian elimination on the above matrix to reduce it to row echelon form or reduced row echelon form.

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Problem 448

15. If $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ is a linear transformation such that $T\left[\begin{array}{l} 1 \\ 4 \end{array}\right]=\left[\begin{array}{r} -2 \\ 22 \end{array}\right] \quad \text { and } \quad T\left[\begin{array}{r} 2 \\ -3 \end{array}\right]=\left[\begin{array}{r} 18 \\ -11 \end{array}\right]$ find the matrix that induces this transformation.

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Problem 449

Homework: HW \#14: Sections 11.1-11.2 Question 21, 11.2.11-T HW Score: $54.52 \%, 16.36$ of 30 points Points: 0 of 1 Save
Question list Question 21 Question 22 Question 23 Question 24 x/s Question 25 Question 26
The accompanying table shows results of challenged referee calls in a major tennis tournament. Use a 0.05 significance level to test the claim that the gender of the tennis player is independent of whether a call is overturned.
Click the icon to view the table. A. $\mathrm{H}_{0}$ : The gender of the tennis player is not independent of whether a call is overturned. $\mathrm{H}_{1}$ : The gender of the tennis player is independent of whether a call is overturned. $\mathrm{H}_{0}$ : Male tennis players are more successful in overturning calls than female players. $\mathrm{H}_{1}$ : Male tennis players are not more successful in overturning calls than female players. . $\mathrm{H}_{0}$ : Male tennis players are not more successful in overturning calls than female players $\mathrm{H}_{1}$ : Male tennis players are more successful in overturning calls than female players. $\mathrm{H}_{0}$ : The gender of the tennis player is independent of whether a call is overturned. $\mathrm{H}_{1}$ : The gender of the tennis player is not independent of whether a call is overturned.
Determine the test statistic $\chi^{2}=$ $\square$ (Round to three decimal places as needed.) Print Done \begin{tabular}{|l|c|c} \hline & \multicolumn{2}{|c}{ Was the Challenge to the Call Successful? } \\ \hline & Yes & No \\ \hline Men & 343 & 719 \\ \hline Women & 462 & 825 \\ \hline \end{tabular} $\qquad$ $\sqrt[1]{11}$ 7 (1,1) Clear all Check answer View an example Get more help -

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Problem 450

abes warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then independent of the choice for the
Question 23 Question 24 Question 25 Question 26 $x / 5$ Question 27 Question 28 \begin{tabular}{l|ccc} & Human activity & Natural patterns & Don't know \\ \hline Male & 344 & 140 & 40 \\ Female & 333 & 166 & 37 \end{tabular}
Click here to view the chi-square distribution table. $\qquad$ $\qquad$ Identify the null and alternative hypotheses. $\mathrm{H}_{0}$ : $\square$ d $\square$ $\mathrm{H}_{1}$ : $\square$ $\square$

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Problem 451

Example Find the characteristic equation of $A = \begin{bmatrix} 5 & -2 & 6 & -1 \\ 0 & 2 & -8 & 0 \\ 0 & 0 & 5 & 1 \\ 0 & 0 & 0 & 1 \end{bmatrix}$ The eigenvalues of a triangular matrix are the entries on its main diagonal.

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Problem 452

Given $A = \begin{pmatrix} 1 & 1 & 2 \\ 0 & 2 & 1 \\ 0 & 0 & 3 \end{pmatrix}$ . Find the eigen values and eigen vector for this matrix.

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Problem 453

If $A = \begin{bmatrix} b & 2 & -1 \\ 3 & 1 & -1 \\ -1 & 0 & 3 \end{bmatrix}$ and $\begin{bmatrix} 1 \\ \alpha \\ 1 \end{bmatrix}$ is an eigenvector of the matrix $A$ , then $b =$
Answer:

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Problem 454

If $A=\left[\begin{array}{lll}0 & 3 & 0 \\ 0 & 0 & b \\ 9 & 0 & 0\end{array}\right]$ then one of the following is an eigenvalue of $A$

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Problem 455

If $A=\left[\begin{array}{lll}0 & 3 & 0 \\ 0 & 0 & b \\ 9 & 0 & 0\end{array}\right]$ then one of the following is an eigenvalue of $A$
Select one: $2 b$ $3 \sqrt[3]{b}$ $2 \sqrt{3 b}$ $3 b$

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Problem 456

If $A = \begin{bmatrix} 0 & 3 & 0 \\ 0 & 0 & b \\ 9 & 0 & 0 \end{bmatrix}$ then one of the following is an eigenvalue of $A$
Select one: $2\sqrt{3b}$ $3\sqrt[3]{b}$ $3b$ $2b$

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Problem 457

If $A = \begin{bmatrix} b & 2 & -1 \\ -1 & 3 & 1 \\ 0 & 1 & 2 \\ 3 & -1 & -1 \end{bmatrix}$ and $\begin{bmatrix} p \\ q \\ 1 \end{bmatrix}$ is an eigenvector of the matrix $A$ , then $b =$ Answer:

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Problem 458

Q: If $\left|\begin{array}{ccc}1 & 1 & 5 \\ 6 & -1 & 2 \\ 3 & a & 3\end{array}\right|=2$ , then $\left|\begin{array}{ccc}1 & 2 b & 3 \\ 1 & -2 & n \\ 5 & 4 & 3\end{array}\right|=$ ?

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Problem 459

If $T: \mathbb{R}^{2} \rightarrow \mathbb{R}^{2}$ is a linear transformation such that $T\left(\left[\begin{array}{l} 1 \\ 0 \end{array}\right]\right)=\left[\begin{array}{c} -8 \\ 7 \end{array}\right], \quad T\left(\left[\begin{array}{l} 0 \\ 1 \end{array}\right]\right)=\left[\begin{array}{l} -10 \\ -10 \end{array}\right]$ then the standard matrix of $T$ is $A=\left[\begin{array}{cc} \boxed{-8} & -10 \\ \boxed{7} & \boxed{-10} \end{array}\right]$

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Problem 460

Find the value of the determinant. $\left|\begin{array}{ll} -1 & 3 \\ -5 & 3 \end{array}\right|$
The value of the determinant is $\square$

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Problem 461

Consider a U.S. economy consisting of 4 sectors: (1) Textiles, (2) Apparel, (3) Farms, and (4) Wholesale Trade. The following $(I-A)^{-1}$ matrix was computed from an input-output table for this economy: $(I-A)^{-1}=\left[\begin{array}{cccc} 1.2197 & 0.1723 & 0.0006 & 0.0038 \\ 0.0134 & 1.070 & 0 & 0.0011 \\ 0.0875 & 0.0123 & 1.2047 & 0.0022 \\ 0.0050 & 0.0007 & -0.0034 & 1.0413 \end{array}\right]$
What is the interpretation of the 3,2 -entry of $(I-A)^{-1}$ ? a. It takes $\$ 0.0123$ worth of goods from the Farms sector to produce $\$ 1$ worth of Apparel sector goods. b. The Farms sector must increase production by $\$ 0.0123$ in order to meet a $\$ 1$ increase in demand in the Apparel sector. c. The Apparel sector must increase production by $\$ 0$ in order to meet a $\$ 1$ increase in demand in the Farms sector. d. It takes $\$ 0$ worth of goods from the Apparel sector to produce $\$ 1$ worth of the Farms sector goods.

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Problem 462

Find the steady-state vector for the transition matrix. $\begin{bmatrix} \frac{6}{7} & \frac{2}{7} \\ \frac{1}{7} & \frac{5}{7} \end{bmatrix}$ x = $\begin{bmatrix} \rule{0.5cm}{0.15mm} \\ \rule{0.5cm}{0.15mm} \end{bmatrix}$

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Problem 463

Find the positive predictive value of a polygraph test: P(Lied | Positive) using the data: 13 No, 45 Yes, 30 No, 12 Yes.

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Problem 464

Calculate the correlation $r$ between Amazon and B\&N prices for 14 textbooks. Round to the nearest 0.001.

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Problem 465

Subtract the matrices. $\begin{bmatrix} 8 & 2 & -8 \\ -9 & -8 & 4 \\ 9 & 9 & -2 \end{bmatrix} - \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 5 \\ 2 & 1 & -1 \end{bmatrix}$

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Problem 466

Employing elementary row transformations, find the inverse of the matrix $\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix}$

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Problem 467

$S=\left[\begin{array}{llll} -9 & 4 & -7 & -6 \end{array}\right]$
The additive inverse is $\square$ (Simplify your answer.)

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Problem 468

Give an example of a $2 \times 2$ matrix that is its own inverse.
An example of a $2 \times 2$ matrix that is its own inverse is $\square$

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Problem 469

Part 1 of 2 a. Use the coding matrix $\mathrm{A}=\left[\begin{array}{rr}2 & -1 \\ 5 & -3\end{array}\right]$ to encode the word LIFT. b. Use its inverse, $A^{-1}=\left[\begin{array}{ll}3 & -1 \\ 5 & -2\end{array}\right]$ , to decode $11,25,-16,-49$ . a. The encoded message is $\square$ (Type the values in the correct order, separated by commas.) Help me solve this View an example Get more help - Review Progress

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Problem 470

View the accompanying description of how messages are being represented as matrices which are then encoded with matrix multiplication. The matrix $\left[\begin{array}{rrrrrr}56 & 51 & 116 & 65 & 87 & 149 \\ 18 & 120 & 80 & 102 & 102 & 164 \\ 101 & 24 & 154 & 43 & 111 & 162\end{array}\right]$ was encoded using the matrix $A=\left[\begin{array}{rrr}1 & 3 & 2 \\ 4 & 6 & -2 \\ 0 & 1 & 5\end{array}\right]$ What is the message? (i) Click the icon to learn how to convert a message into a matrix that can be encoded.
Write the message below. $\square$ $"$ "
Help me solve this View an example Get more help -

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Problem 471

Question3: Given matrices: $A=\left(\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right), B=\left(\begin{array}{rr}3 & -5 \\ -1 & 2\end{array}\right)$ , Find the determinant of $A, A+B$ and $A B$

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Problem 472

Question 12. Given matrices $A=\left(\begin{array}{lll} 2 & 0 & 1 \\ 3 & 0 & 0 \\ 5 & 1 & 1 \end{array}\right) \quad B=\left(\begin{array}{lll} 1 & 0 & 1 \\ 1 & 2 & 1 \\ 1 & 1 & 0 \end{array}\right),$
Evaluate the following: a) Transpose of B, b) Determinant of A , c) $A+2 B$ , d) $A-B$ , e) $A B$

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Problem 473

Find a basis for the eigenspace corresponding to the eigenvalue. $A=\left[\begin{array}{rrr} 3 & 3 & -2 \\ 2 & 8 & -4 \\ -2 & -6 & 6 \end{array}\right], \lambda=2$
A basis for the eigenspace corresponding to $\lambda=2$ is $\square$ (Type a vector or list of vectors. Type an integer or simpantied fraction for each matrix element. Use a comma to separate answers as needed)

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Problem 474

6. Prove that the matrix $A^{-2}$ is symmetricir eimen
7. If $\mathbf{A}$ be any square matrix then show that $\mathbf{A}+\mathbf{A}^{\prime}$ is symmetric and $\mathbf{A}-\mathbf{A}^{\prime}$ is skew-symmetric.
8. If $\mathbf{A}$ is a skew-Hermitian matrix, then show that $i \mathbf{A}$ is Hermitian.
9. If $\mathbf{A}, \mathbf{B}$ are symmetric (skew-symmetric) matrices of the same order, then so is also $\mathbf{A}+\mathbf{B}$ .
10. Show that the matrix $\mathbf{B}^{\theta} \mathbf{A B}$ is Hermitian or skew-hermitian according as $\mathbf{A}$ is Hermitian or skew-Hermitian. (Kanpur 2014
11. Show that all positive integral powers of a symmetric matrix are symmetric.
12. If $A$ and $B$ are symmetric matrices of ordern, then show that $A B+B A$ is symmetric ar $\mathrm{AB}-\mathrm{BA}$ is skew-symmetric. (Lucknow 200

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Problem 475

6. Prove that the matrix $A^{-2}$ is symmetricir eimen
7. If $\mathbf{A}$ be any square matrix then show that $\mathbf{A}+\mathbf{A}^{\prime}$ is symmetric and $\mathbf{A}-\mathbf{A}^{\prime}$ is skew-symmetric.
8. If $\mathbf{A}$ is a skew-Hermitian matrix, then show that $i \mathbf{A}$ is Hermitian.
9. If $\mathbf{A}, \mathbf{B}$ are symmetric (skew-symmetric) matrices of the same order, then so is also $\mathbf{A}+\mathbf{B}$ .
10. Show that the matrix $\mathbf{B}^{\theta} \mathbf{A B}$ is Hermitian or skew-hermitian according as $\mathbf{A}$ is Hermitian or skew-Hermitian. (Kanpur 2014
11. Show that all positive integral powers of a symmetric matrix are symmetric.
12. If $A$ and $B$ are symmetric matrices of ordern, then show that $A B+B A$ is symmetric ar $\mathrm{AB}-\mathrm{BA}$ is skew-symmetric. (Lucknow 200

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Problem 476

which has products that are the Shade the yellow shaded numbers in each row.
2. What pattern do you see? \begin{tabular}{|c|c|c|c|c|c|c|c|c|c|} \hline $x$ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline 1 & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline 2 & 2 & 4 & 6 & 8 & 10 & 12 & 14 & 16 & 18 \\ \hline 3 & 3 & 6 & 9 & 12 & 15 & 18 & 21 & 24 & 27 \\ \hline 4 & 4 & 8 & 12 & 16 & 20 & 24 & 28 & 32 & 36 \\ \hline 5 & 5 & 10 & 15 & 20 & 25 & 30 & 35 & 40 & 45 \\ \hline 6 & 6 & 12 & 18 & 24 & 30 & 36 & 42 & 48 & 54 \\ \hline 7 & 7 & 14 & 21 & 28 & 35 & 42 & 49 & 56 & 63 \\ \hline 8 & 8 & 16 & 24 & 32 & 40 & 48 & 56 & 64 & 72 \\ \hline 9 & 9 & 18 & 27 & 36 & 45 & 54 & 63 & 72 & 81 \\ \hline \end{tabular}
3. Explain why this pattern is true.

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Problem 477

A is a $3 \times 3$ matrix with three pivot positions. Does $A \mathbf{x}=\mathbf{0}$ have a nontrivial solution?

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Problem 478

Check if the matrix columns are linearly independent. Use the matrix:
$\left[\begin{array}{rrr} -4 & -3 & 0 \\ 0 & -1 & 6 \\ 1 & 1 & -6 \\ 2 & 1 & -12 \end{array}\right]$
Choose A, B, C, or D and justify your answer.

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Problem 479

Check if the matrix columns are linearly independent.
$\begin{bmatrix} 1 & 2 & -3 & 6 \\ 2 & 5 & -4 & 6 \\ 2 & 7 & 3 & -15 \end{bmatrix}$
Choose A, B, C, or D and fill in any blanks.

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Problem 480

Create an augmented matrix for the system: -3x + 7y = 8 and 5x - 8y = 4. What is the matrix's dimension?

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Problem 481

Create an augmented matrix for the system:
x - 5y + 8z = -2, 8x - 4y + z = 4, 8y - 5z = -4.
What is the dimension of this matrix?

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Problem 482

Solve the linear system from the matrix:
$\left[\begin{array}{rr|r} 1 & 3 & 6 \\ 0 & 1 & -1 \end{array}\right]$
What are the solutions? A, B, or C?

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Problem 483

Children were randomly assigned to one of two groups: One group enrolled in a certain preschool, and one did not enroll. Follow-up studies were d decades to answer the research question of whether attendance at preschool had an effect on high school graduation. The data can be divided to whether the preschool attendance effect is different for males and females. The table shows a summary of the data for females, $\square$ Click the icon to view the technology output. \begin{tabular}{ccc} & Preschool & No Preschool \\ HS Grad & 26 & 7 \\ HS Grad No & 3 & 17 \end{tabular}
Compare the graduation rate for those females who went to preschool with the graduation rate for females who did not go to preschool. A. The graduation rate is higher for those females who did not go to preschool. B. The graduation rates are the same. C. The graduation rate is higher for those females who went to preschool. (b) Test the hypothesis that preschool and graduation rate are associated, using a significance level of 0.05.
Choose the correct null hypothesis $\left(\mathrm{H}_{0}\right)$ and alternative hypothesis $\left(\mathrm{H}_{\mathrm{a}}\right)$ .

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Problem 484

Diagonalize the following matrix. The real eigenvalues are given to the right of the matrix. $\left[\begin{array}{rrr} 10 & -7 & 3 \\ 12 & -13 & 9 \\ 12 & -18 & 14 \end{array}\right] ; \lambda=2,4,5$
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $\text { For } P=\square, D=\left[\begin{array}{lll} 2 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 5 \end{array}\right]$ (Simplify your answer.) B. The matrix cannot be diagonalized.

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Problem 485

10. Reduce the matrix $A$ to its normal form, when $A=\left[\begin{array}{cccc}0 & 1 & 2 & -1 \\ 1 & 0 & 1 & 1 \\ 3 & 1 & 0 & 2 \\ 1 & 1 & -2 & 0\end{array}\right]$ . Hence, find the rank of $A$ .

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Problem 486

$\begin{array}{l} \left.\begin{array}{ccc} 3 & 1 & -1 \\ \text { tions -matriges } \end{array}\right] \quad B=\left[\begin{array}{cc} 1 & 6 \\ 3 & -5 \\ -2 & 4 \end{array}\right] \quad C=\left[\begin{array}{cc} 4 & -6 \\ 1 & 2 \end{array}\right] \quad \text { F } \\ =\left[\begin{array}{ccc} 3 & 1 & -1 \\ 2 & 0 & 3 \\ 2 \times 3 \end{array}\right] \cdot\left[\begin{array}{cc} 1 & 6 \\ 3 & -5 \\ -2 & 4 \end{array}\right]=\left[\begin{array}{cc} 8(1)+1(3)+(-1)(-2) & 9 \\ -4 & 24 \end{array}\right] \\ A=\left[\begin{array}{cc} 1 & 6 \\ 3 & -5 \\ -2 & 4 \end{array}\right] \cdot\left[\begin{array}{ccc} 3 & 1 & -1 \\ 2 & 0 & 3 \\ 2 \times 3 \end{array}\right]=\left[\begin{array}{ccc} 15 & 1 & 17 \\ & & \end{array}\right] \\ 3 \times 2 \end{array}$

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Problem 487

Calculate the determinant. $D=\left|\begin{array}{cc} a & b \\ c & d \end{array}\right|=$ $\qquad$ $D=\left|\begin{array}{ll}a & b \\ c & d\end{array}\right|=$ $\square$ (Simplify your answer.)

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Problem 488

Write the augmented matrix of the given system of equations. $\left\{\begin{array}{r} x-6 y=1 \\ 5 x+3 y=4 \end{array}\right.$
The augmented matrix is $\square$ $\square$ $\square$ $\square$ $\square$ $\square$

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Problem 489

Perform the row operation $\frac{1}{3} R_{1}$ on the matrix below and write the new matrix.
$\left[\begin{array}{rrr|r} 3 & -15 & -6 & 24 \\ 4 & -6 & 6 & 0 \\ 4 & 0 & 1 & 7 \end{array}\right]$

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Problem 490

Perform row operations: (a) $R_{2}=-2 r_{1}+r_{2}$ and (b) $R_{3}=8 r_{1}+r_{3}$ on the matrix $\left[\begin{array}{rrr|r} 1 & -4 & 6 & 3 \\ 2 & -6 & 8 & 4 \\ -8 & 3 & 5 & 4 \end{array}\right]$

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Problem 491

Perform row operations on the matrix: (a) $R_{2}=-2 r_{1}+r_{2}$ , (b) $R_{3}=8 r_{1}+r_{3}$ . Matrix: $\left[\begin{array}{rrr|r} 1 & -4 & 6 & 3 \\ 2 & -6 & 8 & 4 \\ -8 & 3 & 5 & 4 \end{array}\right]$

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Problem 492

A clown made purple and green balloon animals. What is the probability a randomly selected one is green and a dog? Simplify.

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Problem 493

Solve the system from the reduced row-echelon form matrix:
$\left[\begin{array}{rr|r} 1 & 0 & 16 \\ 0 & 1 & 6 \end{array}\right]$
Choose A, B, or C for the solution type.

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Problem 494

Solve the system represented by the augmented matrix in reduced row-echelon form:
$\left[\begin{array}{rrr|r} 1 & 0 & 0 & -1 \\ 0 & 1 & 0 & 4 \\ 0 & 0 & 1 & \frac{1}{2} \end{array}\right]$
Choose A, B, or C and simplify your answers.

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Problem 495

ـ بين لماذا تكون المصفوفة القابلة للإنعكاس (Invertible) يكون لها محدد غير مفري.

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Problem 496

List the eigenvalues of A . The transformation $\mathrm{x} \mapsto \mathrm{Ax}$ is the composition of a rotation and a scaling. Give the angle $\varphi$ of the rotation, where $-\pi<\varphi \leq \pi$ , and give the scale factor $r$ . $A=\left[\begin{array}{rr} -8 \sqrt{3} & 8 \\ -8 & -8 \sqrt{3} \end{array}\right]$
The eigenvalues of A are $\lambda=-8 \sqrt{3}+8 \boldsymbol{i},-8 \sqrt{3}-8 \boldsymbol{i}$ . (Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using radicals and $i$ as needed.) $\varphi=$ $\square$ (Simplify your answer. Type an exact answer, using $\pi$ as needed.)

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Problem 497

0: الويت المبفر 0:18:56 -
The next Four (4) questions refer to this situation: Doctors' practices have been categorized as to being Urban, Rural, or Intermediate. The number of doctors who prescribed tetracycline to at least one patient under the age of 8 were recorded for each of these practice :areas. At level of significant 0.01 . The results are
Crosstabulation
Chi-Square Tests \begin{tabular}{|l|r|r|r|} \hline & \multicolumn{1}{|c|}{ Chi-square } & \multicolumn{1}{c|}{ df } & Asymptotic Significance (2-sided) \\ \hline Pearson Chi-Square & $79.277^{9}$ & 2 & .000 \\ Likelihood Ratio & 95.463 & 2 & 000 \\ N of Valid Cases & 474 & & \\ \hline \end{tabular} a. 0 cells $(0.0 \%)$ have expected count less than 5 . The minimum expected count is 12.30 . Specify the Null hypothesis $H_{0}$ : Doctors prescribe tetracycline and county type are linearly associated. 0 - $\mathrm{H}_{\mathrm{q}}$ : Doctors prescribe tetracycline independent of county type - $\mathrm{H}_{0}$ : Doctors prescribe tetracycline and county type are non-linearly associated 0 $\mathrm{H}_{0}$ : Doctors prescribe tetracycline not independent of county type

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Problem 498

Calculate $5|\mathbf{A}| + |\mathbf{B}|$ for $\mathbf{A}=\begin{pmatrix}0 & 1 \\ -8 & -4\end{pmatrix}$ and $\mathbf{B}=\begin{pmatrix}7 & 1 \\ 0 & -5\end{pmatrix}$ .

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Problem 499

CENGAGE ESID lookup PowerZone Gmail One.IU I All IU Ca... Canvas Customer Enreoll... ESID lookup PowerZone Gmail One.IU I All IU Ca... Canvas 9: Markov Chains and the Theory of Games Search this course the statements true. In the provided box, separate each two-word phrase with a comma but no space. For example: augmented matrix,word application. Spelling counts.
The following image, $X_{0}=\left[\begin{array}{c} p_{1} \\ p_{2} \\ \vdots \\ p_{n} \end{array}\right]$ state 1 staten $\left[\begin{array}{c} \text { state } 1 \\ \cdots \\ \text { state } n \end{array}\left[\begin{array}{ccc} a_{11} & \cdots & a_{1 n} \\ \vdots & \ddots & \vdots \\ a_{n 1} & \cdots & a_{n n} \end{array}\right]\right.$ , represents a $\qquad$ . The next matrix, $\left[\begin{array}{c}p_{1} \\ p_{2} \\ \vdots \\ \vdots \\ p_{n}\end{array}\right]$ called a distribution vector. If $T$ represents the $n \times n$ transition matrix associated with the Markov process, then the probability distribution of the system after $m$ observations is given by $X_{m}=T^{m} X_{0}$
Applied Example 6 Taxi Movement between Zones is called a $\qquad$ . Lastly $X_{m}=T^{m} X_{0}$ , is called a $\qquad$ -
Type your answer here transition matrix, distribution vector,
To keep track of the location of its cabs, Zephyr Cab has divided a town into three zones: Zone I. Zone II. and Zone III. Zephvr's SUBMIT

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Problem 500

Let $A=\left[\begin{array}{ccc}2 & -1 & 3 \\ 1 & 0 & -1 \\ 4 & 1 & 2\end{array}\right]^{\prime}$ , then $(\operatorname{adj}(A))_{12}=$
6
05 $-6$

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Matrix

Problem 401

Problem 402

Evaluate the following determinant. ∣0−65−25−413−2∣\left|\begin{array}{ccc} 0 & -6 & 5 \\ -2 & 5 & -4 \\ 1 & 3 & -2 \end{array}\right|∣∣​0−21​−653​5−4−2​∣∣​

Problem 403

Problem 404

Problem 405

Problem 406

Problem 407

Problem 408

Problem 409

24. Find the value of the determinant. ∣3−462∣\left|\begin{array}{cc} 3 & -4 \\ 6 & 2 \end{array}\right|∣∣​36​−42​∣∣​

Problem 410

Calculate D(CE)D(C E)D(CE) where C=[3−781]C=\begin{bmatrix}3 & -7 \\ 8 & 1\end{bmatrix}C=[38​−71​], D=[9−2]D=\begin{bmatrix}9 & -2\end{bmatrix}D=[9​−2​], E=[−35−72]E=\begin{bmatrix}-3 & 5 \\ -7 & 2\end{bmatrix}E=[−3−7​52​].

Problem 411

Perform the elementary row operation −12R2→R2-\frac{1}{2} R_{2} \rightarrow R_{2}−21​R2​→R2​ on the given matrix. [1234−6−2]\left[\begin{array}{cc:c} 1 & 2 & 3 \\ 4 & -6 & -2 \end{array}\right][14​2−6​3−2​]Resulting matrix:

Problem 412

Perform the elementary row operation −2R1+R2→R2-2 R_{1}+R_{2} \rightarrow R_{2}−2R1​+R2​→R2​ on the given matrix. [4230−6−2]\left[\begin{array}{cc:c} 4 & 2 & 3 \\ 0 & -6 & -2 \end{array}\right][40​2−6​3−2​]Resulting matrix: □\square□

Problem 413

Find the rank of the matrix [−2333I−41−572]\text{Find the rank of the matrix } \begin{bmatrix} -2 & 3 & 3 \\ 3_{\mathrm{I}} & -4 & 1 \\ -5 & 7 & 2 \end{bmatrix}Find the rank of the matrix ⎣⎡​−23I​−5​3−47​312​⎦⎤​

Problem 414

Problem 415

Problem 416

Problem 417

Problem 418

Calculate the determinant DDD of the matrix: [15−3413−21−2−35−335−3−2]\begin{bmatrix}1 & 5 & -3 & 4 \\ 1 & 3 & -2 & 1 \\ -2 & -3 & 5 & -3 \\ 3 & 5 & -3 & -2\end{bmatrix}⎣⎡​11−23​53−35​−3−25−3​41−3−2​⎦⎤​.

Problem 419

Problem 420

Problem 421

Problem 422

Problem 423

Let A=[2230−1−201−1]A = \begin{bmatrix} 2 & 2 & 3 \\ 0 & -1 & -2 \\ 0 & 1 & -1 \end{bmatrix}A=⎣⎡​200​2−11​3−2−1​⎦⎤​. Find det⁡(A+AA−1)\det(A + AA^{-1})det(A+AA−1).6 -2 -6 7 2

Problem 424

If AAA is a 4×44 \times 44×4 matrix with det A=2\text{det } A = 2det A=2, find det(Adj(A))\text{det}(\text{Adj}(A))det(Adj(A)).8 -2 2 12\frac{1}{2}21​ 16

Problem 425

2): suppose a square matrix AAA satisfies A=2A⊤A=2 A^{\top}A=2A⊤ show that A=0A=0A=0

Problem 426

Reduce the matrix to row echelon form:[1−90−10−80100−23000173000000] \begin{bmatrix} 1 & -9 & 0 & -1 & 0 & -8 \\ 0 & 1 & 0 & 0 & -2 & 3 \\ 0 & 0 & 0 & 1 & 7 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{bmatrix} ⎣⎡​1000​−9100​0000​−1010​0−270​−8330​⎦⎤​

Problem 427

Is it true or false that a matrix can be row reduced to multiple reduced echelon forms? Justify your answer.

Problem 428

Problem 429

Problem 430

Complete the sentence below. An mmm by nnn rectangular array of numbers is called a(n) _____.An mmm by nnn rectangular array of numbers is called a(n) column index. matrix. row index. entry.

Problem 431

Complete the sentence below. The matrix used to represent a system of linear equations is called a(n) _______ matrix.The matrix used to represent a system of linear equations is called a(n) _______ matrix. coefficient augmented invertible resulting

Problem 432

Complete the sentence below. The notation a35a_{35}a35​ refers to the entry in the _______ row and _______ column of a matrix.The notation a35a_{35}a35​ refers to the entry in the \_\_\_\_\_ row and \_\_\_\_\_\_ column of a matrix. third fifth

Problem 433

Determine whether the following statement is true or false.The matrix [13−2015000] \begin{bmatrix} 1 & 3 & -2 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{bmatrix} ⎣⎡​100​310​−250​⎦⎤​ is in row echelon form.Choose the correct answer below. True False

Problem 434

Problem 435

Problem 436

Problem 437

Problem 438

Create a 3x3 magic square using the numbers 2, 5, 8, 12, 15, 18, 22, 25, and 28.

Problem 439

Lottery machine outputs digits 0-9 in 200 trials. Find: (a) experimental probability of even numbers, (b) theoretical probability, (c) true statement about trials and probabilities. Round answers to nearest thousandths.

Problem 440

If the price drops by \$1, how much does the total quantity demanded by Michelle, Laura, and Hillary increase? Choices: 4, 5, 2, or 3 units.

Problem 441

Problem 442

Problem 443

Find B-AA=[9291]A = \begin{bmatrix} 9 & 2 \\ 9 & 1 \end{bmatrix}A=[99​21​] B=[−829−9]B = \begin{bmatrix} -8 & 2 \\ 9 & -9 \end{bmatrix}B=[−89​2−9​]B-A=☐

Problem 444

d) Phuntsho factored every multiple of 4 from 4 to 40 into prime factors. He used a matrix to show how many times each prime factor (2,3,5 and 7) appeared in each number. Create Phuntsho's matrix. [2]

Problem 445

Construct an augmented matrix for this linear system: x−y−4z=52x+2z=04x+y+z=3\begin{array}{l} x-y-4 z=5 \\ 2 x+2 z=0 \\ 4 x+y+z=3 \end{array}x−y−4z=52x+2z=04x+y+z=3​ DONE

Problem 446

Problem 447

[a1012200010b]\begin{bmatrix} a & 1 & 0 & 1 \\ 2 & 2 & 0 & \\ 0 & 0 & 1 & 0 \\ b \end{bmatrix}⎣⎡​a20b​120​001​10​⎦⎤​Perform Gaussian elimination on the above matrix to reduce it to row echelon form or reduced row echelon form.

Problem 448

Problem 449

Problem 450

Problem 451

Problem 452

Given A=(112021003)A = \begin{pmatrix} 1 & 1 & 2 \\ 0 & 2 & 1 \\ 0 & 0 & 3 \end{pmatrix}A=⎝⎛​100​120​213​⎠⎞​. Find the eigen values and eigen vector for this matrix.

Problem 453

If A=[b2−131−1−103]A = \begin{bmatrix} b & 2 & -1 \\ 3 & 1 & -1 \\ -1 & 0 & 3 \end{bmatrix}A=⎣⎡​b3−1​210​−1−13​⎦⎤​ and [1α1]\begin{bmatrix} 1 \\ \alpha \\ 1 \end{bmatrix}⎣⎡​1α1​⎦⎤​ is an eigenvector of the matrix AAA, then b=b =b=Answer:

Problem 454

Evaluate the following determinant. $\left|\begin{array}{ccc} 0 & -6 & 5 \\ -2 & 5 & -4 \\ 1 & 3 & -2 \end{array}\right|$

24. Find the value of the determinant. $\left|\begin{array}{cc} 3 & -4 \\ 6 & 2 \end{array}\right|$

Calculate $D(C E)$ where $C=\begin{bmatrix}3 & -7 \\ 8 & 1\end{bmatrix}$ , $D=\begin{bmatrix}9 & -2\end{bmatrix}$ , $E=\begin{bmatrix}-3 & 5 \\ -7 & 2\end{bmatrix}$ .

Perform the elementary row operation $-\frac{1}{2} R_{2} \rightarrow R_{2}$ on the given matrix. $\left[\begin{array}{cc:c} 1 & 2 & 3 \\ 4 & -6 & -2 \end{array}\right]$
Resulting matrix:

Perform the elementary row operation $-2 R_{1}+R_{2} \rightarrow R_{2}$ on the given matrix. $\left[\begin{array}{cc:c} 4 & 2 & 3 \\ 0 & -6 & -2 \end{array}\right]$
Resulting matrix:
$\square$

$\text{Find the rank of the matrix } \begin{bmatrix} -2 & 3 & 3 \\ 3_{\mathrm{I}} & -4 & 1 \\ -5 & 7 & 2 \end{bmatrix}$

Calculate the determinant $D$ of the matrix: $\begin{bmatrix}1 & 5 & -3 & 4 \\ 1 & 3 & -2 & 1 \\ -2 & -3 & 5 & -3 \\ 3 & 5 & -3 & -2\end{bmatrix}$ .

Let $A = \begin{bmatrix} 2 & 2 & 3 \\ 0 & -1 & -2 \\ 0 & 1 & -1 \end{bmatrix}$ . Find $\det(A + AA^{-1})$ .
6 -2 -6 7 2

If $A$ is a $4 \times 4$ matrix with $\text{det } A = 2$ , find $\text{det}(\text{Adj}(A))$ .
8 -2 2 $\frac{1}{2}$ 16

2): suppose a square matrix $A$ satisfies $A=2 A^{\top}$ show that $A=0$

Reduce the matrix to row echelon form:
$\begin{bmatrix} 1 & -9 & 0 & -1 & 0 & -8 \\ 0 & 1 & 0 & 0 & -2 & 3 \\ 0 & 0 & 0 & 1 & 7 & 3 \\ 0 & 0 & 0 & 0 & 0 & 0 \end{bmatrix}$

Complete the sentence below. An $m$ by $n$ rectangular array of numbers is called a(n) _____.
An $m$ by $n$ rectangular array of numbers is called a(n) column index. matrix. row index. entry.

Complete the sentence below. The matrix used to represent a system of linear equations is called a(n) _ matrix.
The matrix used to represent a system of linear equations is called a(n) _ matrix. coefficient augmented invertible resulting

Complete the sentence below. The notation $a_{35}$ refers to the entry in the _ row and _ column of a matrix.
The notation $a_{35}$ refers to the entry in the \_\_\_\_\_ row and \_\_\_\_\_\_ column of a matrix. third fifth

Determine whether the following statement is true or false.
The matrix $\begin{bmatrix} 1 & 3 & -2 \\ 0 & 1 & 5 \\ 0 & 0 & 0 \end{bmatrix}$ is in row echelon form.
Choose the correct answer below. True False

Find B-A
$A = \begin{bmatrix} 9 & 2 \\ 9 & 1 \end{bmatrix}$ $B = \begin{bmatrix} -8 & 2 \\ 9 & -9 \end{bmatrix}$
B-A=☐

Construct an augmented matrix for this linear system: $\begin{array}{l} x-y-4 z=5 \\ 2 x+2 z=0 \\ 4 x+y+z=3 \end{array}$ DONE

$\begin{bmatrix} a & 1 & 0 & 1 \\ 2 & 2 & 0 & \\ 0 & 0 & 1 & 0 \\ b \end{bmatrix}$
Perform Gaussian elimination on the above matrix to reduce it to row echelon form or reduced row echelon form.

Given $A = \begin{pmatrix} 1 & 1 & 2 \\ 0 & 2 & 1 \\ 0 & 0 & 3 \end{pmatrix}$ . Find the eigen values and eigen vector for this matrix.

If $A = \begin{bmatrix} b & 2 & -1 \\ 3 & 1 & -1 \\ -1 & 0 & 3 \end{bmatrix}$ and $\begin{bmatrix} 1 \\ \alpha \\ 1 \end{bmatrix}$ is an eigenvector of the matrix $A$ , then $b =$
Answer:

If $A=\left[\begin{array}{lll}0 & 3 & 0 \\ 0 & 0 & b \\ 9 & 0 & 0\end{array}\right]$ then one of the following is an eigenvalue of $A$

If $A=\left[\begin{array}{lll}0 & 3 & 0 \\ 0 & 0 & b \\ 9 & 0 & 0\end{array}\right]$ then one of the following is an eigenvalue of $A$
Select one: $2 b$ $3 \sqrt[3]{b}$ $2 \sqrt{3 b}$ $3 b$

If $A = \begin{bmatrix} 0 & 3 & 0 \\ 0 & 0 & b \\ 9 & 0 & 0 \end{bmatrix}$ then one of the following is an eigenvalue of $A$
Select one: $2\sqrt{3b}$ $3\sqrt[3]{b}$ $3b$ $2b$

Q: If $\left|\begin{array}{ccc}1 & 1 & 5 \\ 6 & -1 & 2 \\ 3 & a & 3\end{array}\right|=2$ , then $\left|\begin{array}{ccc}1 & 2 b & 3 \\ 1 & -2 & n \\ 5 & 4 & 3\end{array}\right|=$ ?

Find the value of the determinant. $\left|\begin{array}{ll} -1 & 3 \\ -5 & 3 \end{array}\right|$
The value of the determinant is $\square$

Find the steady-state vector for the transition matrix. $\begin{bmatrix} \frac{6}{7} & \frac{2}{7} \\ \frac{1}{7} & \frac{5}{7} \end{bmatrix}$ x = $\begin{bmatrix} \rule{0.5cm}{0.15mm} \\ \rule{0.5cm}{0.15mm} \end{bmatrix}$

Calculate the correlation $r$ between Amazon and B\&N prices for 14 textbooks. Round to the nearest 0.001.

Subtract the matrices. $\begin{bmatrix} 8 & 2 & -8 \\ -9 & -8 & 4 \\ 9 & 9 & -2 \end{bmatrix} - \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & 5 \\ 2 & 1 & -1 \end{bmatrix}$

Employing elementary row transformations, find the inverse of the matrix $\begin{bmatrix} 0 & 1 & 2 \\ 1 & 2 & 3 \\ 3 & 1 & 1 \end{bmatrix}$

$S=\left[\begin{array}{llll} -9 & 4 & -7 & -6 \end{array}\right]$
The additive inverse is $\square$ (Simplify your answer.)

Give an example of a $2 \times 2$ matrix that is its own inverse.
An example of a $2 \times 2$ matrix that is its own inverse is $\square$

Question3: Given matrices: $A=\left(\begin{array}{ll}2 & 5 \\ 1 & 3\end{array}\right), B=\left(\begin{array}{rr}3 & -5 \\ -1 & 2\end{array}\right)$ , Find the determinant of $A, A+B$ and $A B$