Matrices

Problem 101

Find the determinant of the matrix. [007406105]\left[\begin{array}{ccc} 0 & 0 & 7 \\ -4 & 0 & 6 \\ 1 & 0 & -5 \end{array}\right]

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Problem 102

Find the determinant of the matrix. [3131]\left[\begin{array}{ll} 3 & 1 \\ 3 & 1 \end{array}\right]

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Problem 103

Find the determinant of the matrix. [900442645]\left[\begin{array}{ccc} -9 & 0 & 0 \\ 4 & -4 & 2 \\ 6 & 4 & 5 \end{array}\right]

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Problem 104

Step 3: Get a 1 in row 1, column 1
Step 4: Get a 0 in row 2, column 1 [[12.94.48031.237.44]\left[\begin{array}{lll}{\left[\begin{array}{ll}1 & 2.9\end{array}\right.} & 4.48 \\ -0 & -31.2 & -37.44\end{array}\right]
Step 5: Get a 1 in row 2 , column 2 \square \square \square \square \square \square

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Problem 105

Step 4: Get a 0 in row 2, column 1 12.94.48031.237.44]\left.\begin{array}{|lll}\hline 1 & 2.9 & 4.48 \\ \hline 0 & -31.2 & -37.44\end{array}\right]
Step 5: Get a 1 in row 2 , column 2 [12.94.48011.202]\left[\begin{array}{|lll}\hline 1 & 2.9 & 4.48 \\ \hline 0 & 1 & 1.2 \\ \hline 0^{2} & & \end{array}\right]
Step 6: Get a 0 in row 1 , column 2 \square \square \square \square \square \square

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Problem 106

Question 11, 8.2.41 HW Score: 62.5\%, 100 Points: 0 of 1
Solve the following system of equations using matrices (row operations). If the system has no solution, say that it is inconsistent {2x6y=42x+2y=4\left\{\begin{array}{l} 2 x-6 y=-4 \\ 2 x+2 y=4 \end{array}\right.
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution is \square , )) ). (Simplify your answers.) B. There are infinitely many solutions. The solution can be written as {(x,y)x=\{(x, y) \mid x= \square yy is any real number\} (Simplify your answer. Type an expression using yy as the variable.) C. The system is inconsistent.

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Problem 107

augmented matrices for two linear systems in the variables x,yx, y, and zz are given below. 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) [101201280000]\left[\begin{array}{ccc:c} 1 & 0 & 1 & -2 \\ 0 & 1 & 2 & 8 \\ 0 & 0 & 0 & 0 \end{array}\right] The system has no solution. The system has a unique solution. (x,y,z)=(,,)(x, y, z)=(\square, \square, \square) The system has infinitely many solutions.
(x,y,z)=(x,,)(x,y,z)=(,y,)(x,y,z)=(,,z)\begin{array}{l} (x, y, z)=(x, \square, \square) \\ (x, y, z)=(\square, y, \square) \\ (x, y, z)=(\square, \square, z) \end{array} (b) [100200140002]\left[\begin{array}{ccc:c} 1 & 0 & 0 & 2 \\ 0 & 0 & 1 & 4 \\ 0 & 0 & 0 & -2 \end{array}\right] The system has no solution. The system has a unique solution. (x,y,z)=(x, y, z)= \square \square , \square \square The system has infinitely many solutions. (x,y,z)=(x,,)(x, y, z)=(x, \square, \square)
(x,y,z)=(,,)(x,y,z)=(Πz)\begin{array}{l} (x, y, z)=(\square, \square, \square) \\ (x, y, z)=(\Pi \square z) \end{array}

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Problem 108

```latex \begin{array}{|c|c|c|c|c|c|} \hline 2 & \times & 14 & \div & & = 15 \\ \hline + & 襐学 & \div & 鄚获 & \times & \\ \hline 2 & & 1 & & 24 & = 24 \\ \hline & & + & 若密 & - & \\ \hline 2 & & & + & 2 & = 3 \\ \hline & y & = 15 & & y = 12 & \\ \hline \end{array}

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Problem 109

ular el siguiente determinante Trabajo A=1234n2123n13212n24321n3nn1n2n31|A|=\left|\begin{array}{cccccc} 1 & 2 & 3 & 4 & \cdots & n \\ 2 & 1 & 2 & 3 & \cdots & n-1 \\ 3 & 2 & 1 & 2 & \cdots & n-2 \\ 4 & 3 & 2 & 1 & \cdots & n-3 \\ \vdots & & & & & \vdots \\ n n-1 & n-2 & n-3 & \cdots & 1 \end{array}\right|

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Problem 110

Find A+BA+B and BAB-A given that A=[610124261052]A=\left[\begin{array}{cccc} 6 & -1 & 0 & -1 \\ 2 & 4 & -2 & 6 \\ 1 & 0 & 5 & -2 \end{array}\right] and B=[105641522871]B=\left[\begin{array}{cccc} 1 & 0 & 5 & -6 \\ 4 & -1 & 5 & -2 \\ 2 & 8 & -7 & 1 \end{array}\right]

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Problem 111

Find aa, and bb given that X=[aa+b5b],Y=[101858]X=\left[\begin{array}{rr}a & a+b \\ -5 & b\end{array}\right], Y=\left[\begin{array}{rr}10 & 18 \\ -5 & 8\end{array}\right], and X=YX=Y. If any answer has multiple solutions, enter the solutions separated with commas ().

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Problem 112

Solve 4Z+12Y=X4 Z+12 Y=X for ZZ if X=[20804] and Y=[14101]X=\left[\begin{array}{rr} 20 & -8 \\ 0 & 4 \end{array}\right] \text { and } Y=\left[\begin{array}{rr} 1 & 4 \\ -10 & 1 \end{array}\right]

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Problem 113

Evaluate the determinant. 333444235\left|\begin{array}{rrr} 3 & 3 & 3 \\ 4 & 4 & 4 \\ -2 & 3 & -5 \end{array}\right|
The answer is \square

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Problem 114

Find the inverse of [3301]\left[\begin{array}{cc}3 & -3 \\ 0 & 1\end{array}\right]. If the inverse does not exist, select "undefined". Write each matrix element in simplest form.

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Problem 115

Find the inverse of [2002]\left[\begin{array}{cc}2 & 0 \\ 0 & -2\end{array}\right]. If the inverse does not exist, select "undefined". Write each matrix element in simplest form.

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Problem 116

Find the inverse of [1111]\left[\begin{array}{cc}-1 & -1 \\ -1 & -1\end{array}\right]. If the inverse does not exist, select "undefined". Write each matrix element in simplest form.

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Problem 117

Find the inverse of [4747]\left[\begin{array}{ll}4 & 7 \\ 4 & 7\end{array}\right]. If the inverse does not exist, select "undefined". Write each matrix element in simplest form.

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Problem 118

346210]+[312415]\left.\begin{array}{cc}3 & 4 \\ 6 & -2 \\ 1 & 0\end{array}\right]+\left[\begin{array}{cc}-3 & 1 \\ 2 & -4 \\ -1 & 5\end{array}\right]

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Problem 119

7. Find the values of x,yx, y and zz in the following scalar multiplication. 4[xy1z]=[12844]-4\left[\begin{array}{cc} x & y \\ -1 & z \end{array}\right]=\left[\begin{array}{cc} -12 & 8 \\ 4 & 4 \end{array}\right]

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Problem 120

1 A = යැයි ගනිමු. මෙහි k යනු තාත්වික නියතයකි. A - 5A + 10 = 1 නම් 2 k සඳහා තිබිය හැකි අගයන් සොයන්න. මෙහි 1 යනු 2×2 ගණයේ ඒකක න්‍යාසයයි. එනයින් k සඳහා ලැබෙන අගයන්ට අදාළ න්‍යාස දෙක A හා A, නම්, A හා A සොයන්න. B= 2 1 2-6 යැයි ගනිමු. ඉහත k සඳහා ලැබෙන වඩා වැඩි අගය සඳහා ලැබෙන න්‍යාසය A, නම්, (A + B ) සොයන්න. (A,+ B) = (A, + B) − 21 බව අපෝහනය කරන්න. එනයින්, (A +B) හි ප්‍රතිලෝම න්‍යාසය සොයන්න.

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Problem 121

example(3) (et A=[104349597]A=\left[\begin{array}{ccc}-1 & 0 & 4 \\ 3 & -4 & 9 \\ -5 & 9 & 7\end{array}\right], Find tra(A)?\operatorname{tra}\left(A^{\top}\right) ?

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Problem 122

Home Work 1 Q1: Let AA and BB be 3×33 \times 3 matrices with det(A)=4\operatorname{det}(A)=4 and det(B)=6\operatorname{det}(B)=6, and let EE be an elementary matrix of type I. Determine the value of each of the following: (a) det(12A)\operatorname{det}\left(\frac{1}{2} A\right) (b) det(B1AT)\operatorname{det}\left(B^{-1} A^{T}\right) (c) det(EA2)\operatorname{det}\left(E A^{2}\right)

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Problem 123

Find the inverse of the following matrix. If no inverse exists, enter None. A=[41025]A=\left[\begin{array}{rr} 4 & 10 \\ 2 & 5 \end{array}\right]

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Problem 124

D=[102234567]D = \begin{bmatrix} 1 & 0 & 2 \\ 2 & -3 & 4 \\ 5 & 6 & 7 \end{bmatrix}
Find the determinant of matrix D D .

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Problem 125

Find the product of the following two matrices. [55030525][20]\left[\begin{array}{cc} 5 & -5 \\ 0 & -3 \\ 0 & 5 \\ -2 & 5 \end{array}\right]\left[\begin{array}{c} -2 \\ 0 \end{array}\right]

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Problem 126

(3) Compute AB using the following matrices state that the operation is undefined A=[132201],B=[4121]A=\left[\begin{array}{ccc} -1 & 3 & 2 \\ 2 & 0 & 1 \end{array}\right], \quad B=\left[\begin{array}{cc} 4 & 1 \\ -2 & 1 \end{array}\right] a) AB=[21294b3]A B=\left[\begin{array}{ccc}-2 & 12 & 9 \\ 4 & -b & -3\end{array}\right] b) ABA B is unde fined b) AB=[3401]A B=\left[\begin{array}{ll}3 & 4 \\ 0 & 1\end{array}\right] d) AB=[10282]A B=\left[\begin{array}{cc}-10 & 2 \\ 8 & 2\end{array}\right]

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Problem 127

Write the system of equations as a matrix equation AX=BA X=B, with AA as the coefficient matrix of the system. x2y+4z=82x+6y5z=42x6y+6z=2\begin{array}{rr} x-2 y+4 z= & -8 \\ 2 x+6 y-5 z= & 4 \\ 2 x-6 y+6 z= & 2 \end{array}

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Problem 128

Write the system of equations as a matrix equation AX=B\mathrm{AX}=\mathrm{B}, with A as the coefficient matrix of the system. x+7y=263x+7y=34\begin{array}{r} x+7 y=-26 \\ -3 x+7 y=-34 \end{array} [xy]=\square\left[\begin{array}{l}x \\ y\end{array}\right]= \square

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Problem 129

Evaluate the determinant. 2443\left|\begin{array}{rr} 2 & -4 \\ 4 & 3 \end{array}\right|
The determinant is \square

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Problem 130

Solve the system of equations by using the inverse of the coefficient matrix of the equivalent matrix equation. x+8y=196x+7y=32\begin{array}{r} x+8 y=-19 \\ 6 x+7 y=-32 \end{array}
The inverse of matrix A,A1A, A^{-1}, is \square .
The solution of the system is \square - (Type an ordered pair.)

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Problem 131

Question 14 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test
Fill in the blanks so that the resulting statements are true.
If AA is an m×nm \times n matrix and BB is an n×pn \times p matrix, then ABA B is defined as an \square matrix. To find the product ABA B, the number of \square in matrix A must equal the number of \square in matrix B.

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Problem 132

7.
Neka je A=[2132]\mathbf{A}=\left[\begin{array}{rr}2 & 1 \\ -3 & 2\end{array}\right] i f(x)=x3x+3,g(x)=x24x+7.Tadf(x)=x^{3}-x+3, g(x)=x^{2}-4 x+7 . \operatorname{Tad} vrijedi f(A)=A3A+3I=[98249].f(\mathbf{A})=\mathbf{A}^{3}-\mathbf{A}+3 \mathbf{I}=\left[\begin{array}{rr} -9 & 8 \\ -24 & -9 \end{array}\right] .

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Problem 133

Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists. w3xy3z=2w+xy=45w+2x+z=23x3y+z=10\begin{aligned} w-3 x-y-3 z= & 2 \\ w+x-y= & 4 \\ 5 w+2 x+z= & 2 \\ 3 x-3 y+z= & 10 \end{aligned}
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
\square \square \square A. There is one solution. The solution set is {(,,)}\{(\square, \square, \square)\}. (Simplify your answers.) B. There are infinitely many solutions. The solution set is {,,z)}\{\square, \square, z)\}, where zz is any real number. (Type expressions using zz as the variable. Use integers or fractions for any numbers in the expressions.) \square \square (Type expressions using zz as the variable. Use integers or fractions for any numbers in the expressions.) C. There is no solution. The solution set is \varnothing.

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Problem 134

4. Calcule 1ab+c1bc+a1ca+b\left|\begin{array}{lll}1 & a & b+c \\ 1 & b & c+a \\ 1 & c & a+b\end{array}\right|.

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Problem 135

If (1331)(xy)=4(xy)\left(\begin{array}{ll}1 & 3 \\ 3 & 1\end{array}\right)\binom{x}{y}=4\binom{x}{y} then:

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Problem 136

Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists. 2x+7y13z=13x+9y17z=2x+2y4z=3\begin{array}{rr} 2 x+7 y-13 z= & -1 \\ 3 x+9 y-17 z= & 2 \\ x+2 y-4 z= & 3 \end{array}
Select the correct choice below and fill in any answer boxes within your choice. A. The solution is \square \square , ). (Simplify your answers.) B. There are infinitely many solutions. The solution is \square \square , z), where zz is any real number. (Type expressions using zz as the variable. Use integers or fractions for any numbers in the expressions.) C. There is no solution.

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Problem 137

Here is the augmented matrix: [51072121104513]\left[\begin{array}{ccc:c} 5 & 1 & 0 & -7 \\ -2 & -1 & 2 & 11 \\ 0 & -4 & 5 & 13 \end{array}\right]
Enter the missing coefficients for the row operations. (1) \square R1R1:\cdot R_{1} \rightarrow R_{1}: [1150752121104513]\left[\begin{array}{ccc:c}1 & \frac{1}{5} & 0 & -\frac{7}{5} \\ -2 & -1 & 2 & 11 \\ 0 & -4 & 5 & 13\end{array}\right] (2) \square R1+R2R2:\cdot R_{1}+R_{2} \rightarrow R_{2}: [115075035241504513]\left[\begin{array}{ccc:c}1 & \frac{1}{5} & 0 & -\frac{7}{5} \\ 0 & -\frac{3}{5} & 2 & \frac{41}{5} \\ 0 & -4 & 5 & 13\end{array}\right] [1107]\left[\begin{array}{lll:l}1 & \frac{1}{-} & 0 & -\frac{7}{-}\end{array}\right]

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Problem 138

Let D=[067545]D=\left[\begin{array}{cc}0 & 6 \\ -7 & -5 \\ -4 & 5\end{array}\right]. Find 2D2 D. 2D=2 D=

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Problem 139

Compute: [4533]+[3425]\left[\begin{array}{cc}-4 & 5 \\ -3 & -3\end{array}\right]+\left[\begin{array}{cc}3 & -4 \\ -2 & -5\end{array}\right] []\left[\begin{array}{cc} \square & \square \\ \square & \square \end{array}\right]

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Problem 140

Solve the system of equations using determinants x+3y=73x4y=1\begin{aligned} x+3 y & =7 \\ -3 x-4 y & =-1 \end{aligned}

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Problem 141

15 deluxe, and 16 super-deluxe for a $1094\$ 1094 commission. The third week she sells 8 standard, 7 deluxe, and 14 super-deluxe, earning $782\$ 782 in commission. (a) Let x,yx, y, and zz represent the commission she earns on standard, deluxe, and super-deluxe, respectively. Translate the given information into a system of equations in x,yx, y, and zz. (b) Express the system of equations you found in part (a) as a matrix equation of the form AX=BA X=B. \square \square \square \square Watch It \square \square \square \square \square \square [xyz]=\left[\begin{array}{l} x \\ y \\ z \end{array}\right]= \square (c) Find the inverse of the coefficient matrix AA and use it to solve the matrix equation in part (b). \square \square \square \square \square \square A1=A^{-1}= \square \square \square

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Problem 142

Official Time: 15:10:03
Question 1 [10 points] Consider the following matrix AA : A=[51010121354366]A=\left[\begin{array}{ccc} 5 & -10 & 10 \\ -1 & 2 & 1 \\ 3 & -5 & 4 \\ -3 & 6 & -6 \end{array}\right]
For each of the following vectors, determine whether the vector is in the image of AA. If so, demonstrate this by providing a vector x\mathbf{x} so that Ax=biA \mathbf{x}=\mathbf{b}_{\mathbf{i}}. b1=[2041112]b1 is in im(a): A[000]=b1\mathbf{b}_{1}=\left[\begin{array}{c} 20 \\ -4 \\ 11 \\ -12 \end{array}\right] \quad \begin{array}{c} \mathbf{b}_{1} \text { is in im(a): } \\ A\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]=\mathbf{b}_{1} \end{array} b2=[5433]b2 is in im (a):b3=[000]=b2b3=[91066]b3 is in im (a):[000]=b3\begin{array}{l} \mathbf{b}_{2}=\left[\begin{array}{c} -5 \\ 4 \\ -3 \\ 3 \end{array}\right] \quad \begin{array}{c} b_{2} \text { is in im }(a): \\ b_{3}=\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]=b_{2} \\ b_{3}=\left[\begin{array}{c} 9 \\ -10 \\ 6 \\ -6 \end{array}\right] \\ b_{3} \text { is in im }(a): \\ {\left[\begin{array}{l} 0 \\ 0 \\ 0 \end{array}\right]=b_{3}} \end{array} \end{array} SUBMIT AND MARK SAVE AND GLOSE

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Problem 143

The following line of code has already been entered: X=[123]X=\left[\begin{array}{lll}1 & 2 & 3\end{array}\right]; What line of code would you put to set ZZ equals to [123123123]\left[\begin{array}{lll}1 & 2 & 3 \\ 1 & 2 & 3 \\ 1 & 2 & 3\end{array}\right] ?
Make sure you put space in between arguments even though some answers for this problem is acceptable without spaces in actual MATLAB coding. No space in your code.
Your answer starts with Z as follows: Z=\mathrm{Z}= (your line of coding)

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Problem 144

Find the inverse of matrix A using row operations: A=[112312231] A=\begin{bmatrix} 1 & -1 & 2 \\ 3 & 1 & 2 \\ 2 & 3 & -1 \end{bmatrix}

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Problem 145

Explore the stress-energy tensor TαβT_{\alpha \beta} defined by
Tαβ=(ρ0000p0000p0000p) T_{\alpha \beta}=\begin{pmatrix} \rho & 0 & 0 & 0 \\ 0 & p & 0 & 0 \\ 0 & 0 & p & 0 \\ 0 & 0 & 0 & p \end{pmatrix}
with ρ\rho as energy and pp as pressure.

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Problem 146

Find the determinant Δ=αβγβγαγαβ\Delta=\left|\begin{array}{ccc}\alpha & \beta & \gamma \\ \beta & \gamma & \alpha \\ \gamma & \alpha & \beta\end{array}\right| for roots α,β,γ\alpha, \beta, \gamma of x3+ax2+b=0x^{3}+ax^{2}+b=0.

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Problem 147

Prove the system y=Ayy' = A y is solvable when A=[ab0c]A = \begin{bmatrix} a & b \\ 0 & c \end{bmatrix} is upper triangular.

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Problem 148

Show that the system y=Ay\mathbf{y}^{\prime}=A \mathbf{y} can be solved directly for a 2×22 \times 2 upper triangular matrix AA with constant entries. Use the form [xy]=[ab0c][xy]\left[\begin{array}{l} x \\ y \end{array}\right]^{\prime}=\left[\begin{array}{ll} a & b \\ 0 & c \end{array}\right]\left[\begin{array}{l} x \\ y \end{array}\right] and solve the second equation first.

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Problem 149

Find the inverse of the matrix A=[111011001]A = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 1 & 1 \\ 0 & 0 & 1 \end{bmatrix}.

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Problem 150

Cari nilai x+yx + y jika matriks songsang bagi (1437)\left(\begin{array}{cc}1 & 4 \\ -3 & -7\end{array}\right) ialah 1x(743y)\frac{1}{x}\left(\begin{array}{rr}-7 & -4 \\ 3 & y\end{array}\right).

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Problem 151

Calculate the product of the matrices: (1065)\left(\begin{array}{cc}-1 & 0 \\ 6 & -5\end{array}\right) and (2431)\left(\begin{array}{ll}-2 & 4 \\ -3 & 1\end{array}\right).

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Problem 152

Cari nilai x+yx+y jika matriks songsang bagi (1437)\left(\begin{array}{cc}1 & 4 \\ -3 & -7\end{array}\right) adalah 18(743y)\frac{1}{8}\left(\begin{array}{rr}-7 & -4 \\ 3 & y\end{array}\right).

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Problem 153

Cari nilai x+yx+y jika matriks songsang bagi (1437)\left(\begin{array}{cc}1 & 4 \\ -3 & -7\end{array}\right) ialah 18(743y)\frac{1}{8}\left(\begin{array}{rr}-7 & -4 \\ 3 & y\end{array}\right).

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Problem 154

Given matrix A=[123123021]A = \left[\begin{array}{ccc}1 & 2 & 3 \\ 1 & -2 & -3 \\ 0 & 2 & 1\end{array}\right], find A|A|, cofactors, adjoint, and inverse.

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Problem 155

Compute (i) A(B+C)A(B+C) and (ii) (B+C)A(B+C)A for matrices A=(1234)A=\begin{pmatrix}1 & 2 \\ 3 & 4\end{pmatrix}, B=(2142)B=\begin{pmatrix}2 & 1 \\ 4 & 2\end{pmatrix}, C=(5174)C=\begin{pmatrix}5 & 1 \\ 7 & 4\end{pmatrix}.

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Problem 156

Use the Gauss-Jordan method to solve the system of equations. 5x+2y+z=1610x+4y+2z=3215x225y125z=1625\begin{aligned} 5 x+2 y+z & =16 \\ 10 x+4 y+2 z & =32 \\ -\frac{1}{5} x-\frac{2}{25} y-\frac{1}{25} z & =-\frac{16}{25} \end{aligned}
Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The solution is \square , \square, \square ), in the order x,y=zx, y=z. (Simplify your answers.) B. There are infinitely many solutions. The solution is \square ,y,z), y, z), in the order x,y,zx, y, z, where yy and zz are any real numbers. -(Simplify your answer. Use integers or fractions for any numbers in the expression.) C. There is no solution.

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Problem 157

Find the reduced echelon form of this augmented matrix [329100113250338200]\left[\begin{array}{cccc} 3 & -2 & 9 & 100 \\ -1 & 1 & -3 & 250 \\ -3 & 3 & -8 & 200 \end{array}\right]

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Problem 158

Find the reduced row echelon form of this augmented matrix [113250012350013400]\left[\begin{array}{cccc} 1 & -1 & 3 & 250 \\ 0 & 1 & -2 & 350 \\ 0 & -1 & 3 & 400 \end{array}\right]

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Problem 159

6. If AA and BB are square matrices of order 3×33 \times 3 and their determinant values are A=1|A|=-1 and B|B| =3=3, find the value of 3AB|3 \mathrm{AB}|. a. 27 b. -9 C. -3 d. 81 e. -81

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Problem 160

a. 27 b. -9 C. -3 d. 81
7. The values of A,B\mathrm{A}, \mathrm{B} and C in the determinantal equation 2A0011B0523C=0\left|\begin{array}{ccc}2-A & 0 & 0 \\ 1 & 1-B & 0 \\ 5 & 2 & 3-C\end{array}\right|=0 are: a. A=3, B=1,C=2\mathrm{A}=3, \mathrm{~B}=1, \mathrm{C}=2 b. A=2, B=3,C=3\mathrm{A}=2, \mathrm{~B}=3, \mathrm{C}=3 c. A=0, B=1,C=3\mathrm{A}=0, \mathrm{~B}=1, \mathrm{C}=3 d. A=2, B=1,C=3\mathrm{A}=2, \mathrm{~B}=1, \mathrm{C}=3 e. A=2, B=0,C=3\mathrm{A}=2, \mathrm{~B}=0, \mathrm{C}=3

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Problem 161

8. If 11a3=2\left|\begin{array}{ll}1 & 1 \\ a & 3\end{array}\right|=2, then 23111a523=\left|\begin{array}{ccc}-2 & -3 & -1 \\ 1 & -1 & a \\ 5 & 2 & 3\end{array}\right|= ? \square a. 1 b. -1 \qquad c. 3 d. -3 e. 2
9. In the following set of nonhomogeneous equations if z=1z=1, then the value of aa is:

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Problem 162

he augmented matrix for th 4) 3x+5y+7z=575x2y+9z=73x+4y+4z=43\begin{array}{l} 3 x+5 y+7 z=57 \\ 5 x-2 y+9 z=7 \\ 3 x+4 y+4 z=43 \end{array}

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Problem 163

A=[293x]B=[1245]C=[37]D=[t1473245201]A=\left[\begin{array}{ll}2 & 9 \\ 3 & x\end{array}\right] \quad B=\left[\begin{array}{cc}1 & 2 \\ 4 & -5\end{array}\right] \quad C=\left[\begin{array}{c}3 \\ -7\end{array}\right] \quad D=\left[\begin{array}{ccc}t & - & 1 \\ 4 & 7 & 3 \\ -2 & -4 & 5 \\ 2 & 0 & 1\end{array}\right] 1) detA=\operatorname{det} A= 2) detB=\operatorname{det} B= 3) detD=\operatorname{det} D= 4) [A][B]=[A] \cdot[B]= 5) 2A3B=2 A-3 B= 6) [B][C][B][C]

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Problem 164

Find the inverse of the 2×22 \times 2 matrix AA. A=[4523]A=\left[\begin{array}{cc} -4 & -5 \\ 2 & 3 \end{array}\right]

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Problem 165

Let A=[626220630]A=\left[\begin{array}{ccc}6 & 2 & 6 \\ 2 & -2 & 0 \\ 6 & 3 & 0\end{array}\right] and B=[512530771]B=\left[\begin{array}{ccc}5 & 1 & 2 \\ -5 & 3 & 0 \\ 7 & 7 & 1\end{array}\right]. Find 6A2B6 A-2 B. 6A2B=6 A-2 B=

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Problem 166

Here is the augmented matrix: [320702173438]\left[\begin{array}{ccc:c} 3 & 2 & 0 & 7 \\ 0 & -2 & -1 & -7 \\ 3 & 4 & 3 & 8 \end{array}\right]
Enter the missing coefficients for the row operations. (1) II R1R1\cdot R_{1} \rightarrow R_{1} : [12307302173438]\left[\begin{array}{ccc:c}1 & \frac{2}{3} & 0 & \frac{7}{3} \\ 0 & -2 & -1 & -7 \\ 3 & 4 & 3 & 8\end{array}\right] (2) \square R1+R3R3:\cdot R_{1}+R_{3} \rightarrow R_{3}: [12307302170231]\left[\begin{array}{ccc:c}1 & \frac{2}{3} & 0 & \frac{7}{3} \\ 0 & -2 & -1 & -7 \\ 0 & 2 & 3 & 1\end{array}\right]

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Problem 167

Find the production schedule for the technology matrix and demand vector A=[0.30.70.20.10.20.10.81.20.4],D=[754]A=\left[\begin{array}{lll} 0.3 & 0.7 & 0.2 \\ 0.1 & 0.2 & 0.1 \\ 0.8 & 1.2 & 0.4 \end{array}\right] \quad, \quad D=\left[\begin{array}{l} 7 \\ 5 \\ 4 \end{array}\right]

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Problem 168

For each question, you must show all your work: an unjustified correct answer can only get some partial credit. Make sure that you are solving the correct exam for your section. Don't forget to mark each question in Gradescope.
1. Consider the matrix A=[202101252]A=\left[\begin{array}{ccc}2 & 0 & -2 \\ -1 & 0 & 1 \\ -2 & -5 & 2\end{array}\right].

Find the following. a) ( 30 points) The characteristic polynomial pA(λ)p_{A}(\lambda) and three eigenvalues of AA. b) ( 40 points) A basis for the space of solutions of x˙\dot{x}AxA x. c) (30\left(30\right. points) The exponential matrix etAe^{t A}.

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Problem 169

Solve the matrix equation 2X+A=B2 X+A=B for XX if A=[380959]A=\left[\begin{array}{rr}3 & -8 \\ 0 & 9 \\ -5 & 9\end{array}\right] and B=[188433]B=\left[\begin{array}{rr}-1 & -8 \\ 8 & 4 \\ -3 & 3\end{array}\right]. X=X= \square (Simplify your answer.)

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Problem 170

The following table gives an estimate of basic caloric needs for different age groups and activity levels in a county. Complete parts a through c. \begin{tabular}{|c|c|c|c|c|c|c|} \hline Age Range & \multicolumn{2}{|c|}{ Sedentary } & \multicolumn{2}{c|}{ Moderately Active } & \multicolumn{2}{c|}{ Active } \\ \hline & Men & Women & Men & Women & Men & Women \\ \hline 1930\mathbf{1 9 - 3 0} & 2500 & 2100 & 2800 & 2300 & 3200 & 2700 \\ \hline 3150\mathbf{3 1 - 5 0} & 2200 & 1800 & 2500 & 2000 & 2900 & 2200 \\ \hline 51+\mathbf{5 1 +} & 1900 & 1500 & 2100 & 1600 & 2400 & 1900 \\ \hline \end{tabular} a. Use a 3×33 \times 3 matrix, MM, to represent the daily caloric needs, by age and activity level, for men. M=\mathrm{M}=\square (Type an integer or simplified fraction for each matrix element.) b. Use a 3×33 \times 3 matrix, W , to represent the daily caloric needs, by age and activity level, for women. w=\mathrm{w}=\square \square (Type an integer or simplified fraction for each matrix element.) c. Find MWM-W. MW=\mathrm{M}-\mathrm{W}=\square (Type an integer or simplified fraction for each matrix element.)

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Problem 171

Evaluate the determinant. 231351216\left|\begin{array}{rr} \frac{2}{3} & \frac{1}{3} \\ \frac{5}{12} & -\frac{1}{6} \end{array}\right|

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Problem 172

Use Gaussian elimination to find the complete solution to the following system of equations, or show that none exists. {7x+23y+4z=193x+10y+4z=1x+3y4z=1\left\{\begin{array}{rr} 7 x+23 y+4 z= & 19 \\ 3 x+10 y+4 z= & -1 \\ x+3 y-4 z= & 1 \end{array}\right.
Use Gaussian elimination to obtain the matrix in row-echelon form. Choose the correct answer below. A. [13410116400020]\left[\begin{array}{rrr|r}1 & 3 & -4 & 1 \\ 0 & 1 & 16 & -4 \\ 0 & 0 & 0 & 20\end{array}\right] B. [4116403110000]\left[\begin{array}{rrr|r}-4 & 1 & 16 & -4 \\ 0 & 3 & 1 & 1 \\ 0 & 0 & 0 & 0\end{array}\right] C. [11430116400040]\left[\begin{array}{rrr|r}1 & 1 & -4 & 3 \\ 0 & 1 & 16 & -4 \\ 0 & 0 & 0 & 40\end{array}\right] D. [134101164004020]\left[\begin{array}{rrr|r}1 & 3 & -4 & 1 \\ 0 & 1 & 16 & -4 \\ 0 & 0 & 40 & 20\end{array}\right]
Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. There is one solution. The solution set is {(,,)}\{(\square, \square, \square)\}. \square (Simplify your answers. Use integers or fractions for any numbers in the expressions.)
\square B. There are infinitely many solutions. The solution set is {(,,z)}\{(\square, \square, z)\}, where zz is any re:il number. \square (Type expressions using z as the variable. Use integers or fractions for any numbers in the expression.) C. There is no solution. The solution set is \varnothing.

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Problem 173

Solve the system: (2345)(xy)=(713)\begin{pmatrix}2 & -3 \\ 4 & -5\end{pmatrix}\begin{pmatrix}x \\ y\end{pmatrix}=\begin{pmatrix}7 \\ 13\end{pmatrix}.

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Problem 174

Solve the system: (8172)(pq)=(102)\begin{pmatrix} 8 & -1 \\ -7 & 2 \end{pmatrix} \begin{pmatrix} p \\ q \end{pmatrix} = \begin{pmatrix} 10 \\ -2 \end{pmatrix}.

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Problem 175

Solve the system:
(5237)(pq)=(1213) \begin{pmatrix} -5 & 2 \\ 3 & -7 \end{pmatrix} \begin{pmatrix} p \\ q \end{pmatrix} = \begin{pmatrix} 12 \\ -13 \end{pmatrix}

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Problem 176

Solve the system of equations:
(4253)(xy)=(12) \begin{pmatrix} -4 & 2 \\ -5 & 3 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 1 \\ 2 \end{pmatrix}

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Problem 177

Solve the system:
(3458)(xy)=(712) \begin{pmatrix} -3 & 4 \\ -5 & 8 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 7 \\ 12 \end{pmatrix}

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Problem 178

Solve the system:
(4398)(xy)=(611) \begin{pmatrix} 4 & 3 \\ 9 & 8 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} 6 \\ 11 \end{pmatrix}

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Problem 179

Solve the system:
(1234)(xy)=(32) \begin{pmatrix} -1 & 2 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} -3 \\ 2 \end{pmatrix}

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Problem 180

Bestimme, welche der Mengen U1U_{1}, U2U_{2} und U3U_{3} Unterräume von M22(Q)\mathrm{M}_{22}(\mathbb{Q}) sind.

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Problem 181

Use Gaussian elimination to find the complete solution to the system of equations, or show that none exists. {2x+yz=29x+9y8z=9\left\{\begin{array}{l} 2 x+y-z=2 \\ 9 x+9 y-8 z=9 \end{array}\right.
Use Gaussian elimination to obtain the matrix in row-echelon form. Choose the correct answer below. A. [11212101790]\left[\begin{array}{rrr|r}1 & \frac{1}{2} & -\frac{1}{2} & 1 \\ 0 & 1 & -\frac{7}{9} & 0\end{array}\right] B. [192110000]\left[\begin{array}{rrr|r}1 & \frac{9}{2} & -1 & 1 \\ 0 & 0 & 0 & 0\end{array}\right] C. [11212101179]\left[\begin{array}{rrr|r}1 & \frac{1}{2} & -\frac{1}{2} & 1 \\ 0 & 1 & 1 & -\frac{7}{9}\end{array}\right] D. [1127210000]\left[\begin{array}{rrr|r}1 & \frac{1}{2} & -\frac{7}{2} & 1 \\ 0 & 0 & 0 & 0\end{array}\right]

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Problem 182

Let M=[101055]M=\left[\begin{array}{cc} 10 & 10 \\ -5 & -5 \end{array}\right]
Find formulas for the entries of MnM^{n}, where nn is a positive integer. Submit answer Next item

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Problem 183

Use the alternative method for evaluating third-order determinants (finding products along diagonals) to evaluate the determinant. 156145167156145167=\begin{array}{l} \left|\begin{array}{lll} 1 & 5 & 6 \\ 1 & 4 & 5 \\ 1 & 6 & 7 \end{array}\right| \\ \left|\begin{array}{lll} 1 & 5 & 6 \\ 1 & 4 & 5 \\ 1 & 6 & 7 \end{array}\right|=\square \end{array}

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Problem 184

Find A1A^{-1} by forming [A][A \|] and then using row operations to obtain [B][\| B], where A1=[B]A^{-1}=[B]. Check that AA1=IA A^{-1}=I and A1A=IA^{-1} A=I. A=[441031141]A=\left[\begin{array}{rrr} 4 & 4 & -1 \\ 0 & 3 & -1 \\ -1 & -4 & 1 \end{array}\right]
Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. A1=A^{-1}= \square (Type an integer or a simplified fraction for each matrix element.) B. The matrix does not have an inverse.

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Problem 185

Question Given the matrices AA and BB shown below, find 12A4B\frac{1}{2} A-4 B. A=[841041212]B=[340243]A=\left[\begin{array}{ccc} 8 & -4 & -10 \\ 4 & -12 & -12 \end{array}\right] \quad B=\left[\begin{array}{lll} 3 & 4 & 0 \\ 2 & 4 & 3 \end{array}\right]
Answer Attempt 1 out of 3

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Problem 186

Given the matrices AA and BB shown below, find 2B+16A2 B+\frac{1}{6} A. A=[1202418]B=[5572]A=\left[\begin{array}{cc} 12 & 0 \\ -24 & -18 \end{array}\right] \quad B=\left[\begin{array}{cc} 5 & -5 \\ -7 & 2 \end{array}\right]
Answer Attempt 1 out of 3

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Problem 187

n the matrices AA and BB shown below, find 16A+B-\frac{1}{6} A+B. A=[2436]B=[82]A=\left[\begin{array}{l} -24 \\ -36 \end{array}\right] \quad B=\left[\begin{array}{l} -8 \\ -2 \end{array}\right]

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Problem 188

atrices AA and BB shown below, find 5B+A5 B+A. A=[6241]B=[1442]A=\left[\begin{array}{cc} 6 & 2 \\ 4 & -1 \end{array}\right] \quad B=\left[\begin{array}{cc} 1 & 4 \\ -4 & -2 \end{array}\right]

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Problem 189

Eoclogizal Sucessi. St Ben Him County Sch- Play Cinkiti-Enter- f被 Youtube
Addition and Scalar Multiplication of Matrices Score: 8/108 / 10 Penalty ronone
Question Given the matrices AA and BB shown below, find 12B+4A\frac{1}{2} B+4 A. A=[332414]B=[10141014422]A=\left[\begin{array}{cc} 3 & -3 \\ 2 & 4 \\ 1 & 4 \end{array}\right] \quad B=\left[\begin{array}{cc} 10 & -14 \\ -10 & -14 \\ -4 & 22 \end{array}\right]
Answer Attenptiout of 3 Rows: 2ΘΘ2 \Theta \Theta Columns: 2ΘΘ2 \Theta \Theta LogOus

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Problem 190

Given the matrices AA and BB shown below, find 12B+4A\frac{1}{2} B+4 A. A=[332414]B=[10141014422]A=\left[\begin{array}{cc} 3 & -3 \\ 2 & 4 \\ 1 & 4 \end{array}\right] \quad B=\left[\begin{array}{cc} 10 & -14 \\ -10 & -14 \\ -4 & 22 \end{array}\right]

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Problem 191

Given the matrices AA and BB shown below, find A+BA+B. A=[545]B=[403]A=\left[\begin{array}{c} -5 \\ 4 \\ 5 \end{array}\right] \quad B=\left[\begin{array}{c} -4 \\ 0 \\ -3 \end{array}\right]

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Problem 192

16\mathbf{1 6} to 20\mathbf{2 0} refer to the vector equation Ax=λx\mathbf{A} \cdot \mathbf{x}=\lambda \mathbf{x}. For the coefficient matrix A\mathbf{A} given in each case, determine the eigenvalues and an eigenvector corresponding to each eigenvalue: 16A=(211132112)16 \quad \mathbf{A}=\left(\begin{array}{rrr}2 & 1 & 1 \\ 1 & 3 & 2 \\ -1 & 1 & 2\end{array}\right) 17A=(122131221)17 \mathbf{A}=\left(\begin{array}{lll}1 & 2 & 2 \\ 1 & 3 & 1 \\ 2 & 2 & 1\end{array}\right) 18A=(201141120)18 \quad \mathbf{A}=\left(\begin{array}{rrr}2 & 0 & 1 \\ -1 & 4 & -1 \\ -1 & 2 & 0\end{array}\right) 19A=(142031124)19 \mathbf{A}=\left(\begin{array}{rrr}1 & -4 & -2 \\ 0 & 3 & 1 \\ 1 & 2 & 4\end{array}\right) 20A=(303033231)20 \quad \mathbf{A}=\left(\begin{array}{lll}3 & 0 & 3 \\ 0 & 3 & 3 \\ 2 & 3 & 1\end{array}\right)

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Problem 193

Find the inverse of the matrix. [1123240.500.5]\left[\begin{array}{ccc} -1 & -1 & 2 \\ 3 & 2 & -4 \\ -0.5 & 0 & 0.5 \end{array}\right] - [210114212]\left[\begin{array}{lll}2 & 1 & 0 \\ 1 & 1 & 4 \\ 2 & 1 & 2\end{array}\right] [204101222]\left[\begin{array}{lll}2 & 0 & 4 \\ 1 & 0 & 1 \\ 2 & 2 & 2\end{array}\right] [212114211]\left[\begin{array}{lll}2 & 1 & 2 \\ 1 & 1 & 4 \\ 2 & 1 & 1\end{array}\right] [212142112]\left[\begin{array}{lll}2 & 1 & 2 \\ 1 & 4 & 2 \\ 1 & 1 & 2\end{array}\right]

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Problem 194

A=[81517142342]A = \begin{bmatrix} 8 & 1 & 5 \\ -17 & -14 & 2 \\ 3 & 4 & -2 \end{bmatrix} Find det(A)\det(A).

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Problem 195

Find the inverse of the matrix A=[81517142342] A = \left[\begin{array}{rrr}8 & 1 & 5 \\ -17 & -14 & 2 \\ 3 & 4 & -2\end{array}\right] .

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Problem 196

[123346201][xyz]=[278]\left[\begin{array}{ccc}1 & 2 & 3 \\ 3 & 4 & 6 \\ 2 & 0 & -1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}2 \\ 7 \\ 8\end{array}\right]

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Problem 197

ASK YOUR TE
If possible, find ABA B. (If not possible, enter IMPOSSIBLE in any cell of the matrix.) A=[012603516],B=[414516]A=\left[\begin{array}{rrr} 0 & -1 & 2 \\ 6 & 0 & 3 \\ 5 & -1 & 6 \end{array}\right], \quad B=\left[\begin{array}{rr} 4 & -1 \\ 4 & -5 \\ 1 & 6 \end{array}\right] AB=A B= \square \square \square \square \square \square - 1^\hat{1}
State the dimension of the result. (If not possible, enter IMPOSSIBLE in both answer blanks.) \square ×\times \square

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Problem 198

Consider the following. {x15x2+2x3=93x1+x2x3=82x2+5x3=7\left\{\begin{array}{rr} x_{1}-5 x_{2}+2 x_{3}= & -9 \\ -3 x_{1}+x_{2}-x_{3}= & 8 \\ -2 x_{2}+5 x_{3}= & -7 \end{array}\right. (a) Write the system of linear equations as a matrix equation, AX=BA X=B. (b) Use Gauss-Jordan elimination on [AB][A \vdots B] to solve for the matrix XX. X=[x1x2x3]=[]X=\left[\begin{array}{l} x_{1} \\ x_{2} \\ x_{3} \end{array}\right]=\left[\begin{array}{c} \square \\ \square \\ \square \end{array}\right] \Rightarrow

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Problem 199

Ex: Solve the storystem : x1=x2+x3x2=x1+x2x3=x1+x2[011101110]λ111λ111λ=0λ(λ21)λ1=λ2=1λ3=2λ1=1[111011101110][111000000000]δ3=xε2=B,ε1+ε2+ε2=0ε1=Bαδ1=[βαBα]=x[101]+β[110] let x21,β=1x1=[10i]et,x2=[110]et\begin{array}{l} x_{1}^{\prime}=x_{2}+x_{3} \\ x_{2}^{\prime}=x_{1}+x_{2} \\ x_{3}^{\prime}=x_{1}+x_{2} \\ {\left[\begin{array}{lll} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \end{array}\right]} \\ \left|\begin{array}{ccc} -\lambda & 1 & 1 \\ 1 & -\lambda & 1 \\ 1 & 1 & -\lambda \end{array}\right|=0 \quad \begin{array}{l} -\lambda\left(\lambda^{2}-1\right) \\ \lambda_{1}=\lambda_{2}=1 \\ \lambda_{3}=2 \end{array} \\ \lambda_{1}=1 \\ -\left[\begin{array}{lll:l} 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 \end{array}\right] \rightarrow\left[\begin{array}{lll:l} 1 & 1 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array}\right] \\ \delta_{3}=x \text {, } \\ \varepsilon_{2}=B, \varepsilon_{1}+\varepsilon_{2}+\varepsilon_{2}=0 \\ \varepsilon_{1}=-B-\alpha \\ \delta_{1}=\left[\begin{array}{c} -\beta-\alpha \\ B \\ \alpha \end{array}\right] \\ =x\left[\begin{array}{c} -1 \\ 0 \\ 1 \end{array}\right]+\beta\left[\begin{array}{c} -1 \\ 1 \\ 0 \end{array}\right] \\ \text { let } x_{2} 1, \beta=1 \\ x_{1}=\left[\begin{array}{c} -1 \\ 0 \\ i \end{array}\right] e^{-t}, x_{2}=\left[\begin{array}{c} -1 \\ 1 \\ 0 \end{array}\right] e^{-t} \end{array}

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Problem 200

Is [0.82.50.32.5]\left[\begin{array}{l}\frac{0.8}{2.5} \\ \frac{0.3}{2.5}\end{array}\right] the steady state vector for the transition matrix P=[0.70.20.30.8]P=\left[\begin{array}{ll}0.7 & 0.2 \\ 0.3 & 0.8\end{array}\right] ? (Hint: You don't need to solve, there's an easier way.) [This question is based on your assigned pre-reading/prep for the upcoming Assignment] True False

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