QuestionCalculate $34 \cdot \begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix} \cdot \begin{pmatrix} 1 & 7 \\ 3 & 0 \end{pmatrix}$ .

Studdy Solution

STEP 1

Assumptions1. We are given twox matrices. . We are asked to find the product of these matrices.
3. We are also given a scalar multiple of34.
4. Matrix multiplication is associative, meaning that the order in which the matrices are multiplied does not change the result.

STEP 2

First, we need to multiply the two matrices. The product of two matrices A and B is calculated as follows $A \cdot B = \left[\begin{array}{cc}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right] \cdot \left[\begin{array}{cc}b_{11} & b_{12} \\ b_{21} & b_{22}\end{array}\right] = \left[\begin{array}{cc}a_{11}b_{11} + a_{12}b_{21} & a_{11}b_{12} + a_{12}b_{22} \\ a_{21}b_{11} + a_{22}b_{21} & a_{21}b_{12} + a_{22}b_{22}\end{array}\right]$

STEP 3

Now, plug in the given values for the matrices to calculate the product.
$\left[\begin{array}{cc}2 &5 \\ &1\end{array}\right] \cdot \left[\begin{array}{cc}1 &7 \\3 &0\end{array}\right]$

STEP 4

Calculate the product of the two matrices.
$\left[\begin{array}{cc}21 +3 &27 +0 \\41 +13 &47 +10\end{array}\right]$

STEP 5

implify the matrix multiplication.
$\left[\begin{array}{cc}17 &14 \\7 &28\end{array}\right]$

STEP 6

Now that we have the product of the two matrices, we can multiply this by the scalar multiple of34.
$34 \cdot \left[\begin{array}{cc}17 &14 \\ &28\end{array}\right]$

STEP 7

Calculate the product of the scalar multiple and the matrix.
$\left[\begin{array}{cc}3417 &3414 \\347 &3428\end{array}\right]$

STEP 8

implify the scalar multiplication.
$\left[\begin{array}{cc}578 &476 \\238 &952\end{array}\right]$ So, $34\left[\begin{array}{ll}2 &5 \\4 &1\end{array}\right]\left[\begin{array}{ll}1 &7 \\3 &0\end{array}\right]=\left[\begin{array}{cc}578 &476 \\238 &952\end{array}\right]$

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QuestionCalculate $34 \cdot \begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix} \cdot \begin{pmatrix} 1 & 7 \\ 3 & 0 \end{pmatrix}$ .

Studdy Solution

STEP 1

Assumptions1. We are given twox matrices. . We are asked to find the product of these matrices.
3. We are also given a scalar multiple of34.
4. Matrix multiplication is associative, meaning that the order in which the matrices are multiplied does not change the result.

STEP 2

STEP 3

Now, plug in the given values for the matrices to calculate the product.
$\left[\begin{array}{cc}2 &5 \\ &1\end{array}\right] \cdot \left[\begin{array}{cc}1 &7 \\3 &0\end{array}\right]$

STEP 4

Calculate the product of the two matrices.
$\left[\begin{array}{cc}21 +3 &27 +0 \\41 +13 &47 +10\end{array}\right]$

STEP 5

implify the matrix multiplication.
$\left[\begin{array}{cc}17 &14 \\7 &28\end{array}\right]$

STEP 6

Now that we have the product of the two matrices, we can multiply this by the scalar multiple of34.
$34 \cdot \left[\begin{array}{cc}17 &14 \\ &28\end{array}\right]$

STEP 7

Calculate the product of the scalar multiple and the matrix.
$\left[\begin{array}{cc}3417 &3414 \\347 &3428\end{array}\right]$

STEP 8

implify the scalar multiplication.
$\left[\begin{array}{cc}578 &476 \\238 &952\end{array}\right]$ So, $34\left[\begin{array}{ll}2 &5 \\4 &1\end{array}\right]\left[\begin{array}{ll}1 &7 \\3 &0\end{array}\right]=\left[\begin{array}{cc}578 &476 \\238 &952\end{array}\right]$

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QuestionCalculate 34⋅(2541)⋅(1730)34 \cdot \begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix} \cdot \begin{pmatrix} 1 & 7 \\ 3 & 0 \end{pmatrix}34⋅(24​51​)⋅(13​70​).

Studdy Solution

STEP 1

Assumptions1. We are given twox matrices. . We are asked to find the product of these matrices.3. We are also given a scalar multiple of34.4. Matrix multiplication is associative, meaning that the order in which the matrices are multiplied does not change the result.

STEP 2

STEP 3

Now, plug in the given values for the matrices to calculate the product.[251]⋅[1730]\left[\begin{array}{cc}2 &5 \\ &1\end{array}\right] \cdot \left[\begin{array}{cc}1 &7 \\3 &0\end{array}\right][2​51​]⋅[13​70​]

STEP 4

Calculate the product of the two matrices.[2∗1+∗32∗7+∗04∗1+1∗34∗7+1∗0]\left[\begin{array}{cc}2*1 +*3 &2*7 +*0 \\4*1 +1*3 &4*7 +1*0\end{array}\right][2∗1+∗34∗1+1∗3​2∗7+∗04∗7+1∗0​]

STEP 5

implify the matrix multiplication.[1714728]\left[\begin{array}{cc}17 &14 \\7 &28\end{array}\right][177​1428​]

STEP 6

Now that we have the product of the two matrices, we can multiply this by the scalar multiple of34.34⋅[171428]34 \cdot \left[\begin{array}{cc}17 &14 \\ &28\end{array}\right]34⋅[17​1428​]

STEP 7

Calculate the product of the scalar multiple and the matrix.[34∗1734∗1434∗734∗28]\left[\begin{array}{cc}34*17 &34*14 \\34*7 &34*28\end{array}\right][34∗1734∗7​34∗1434∗28​]

STEP 8

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QuestionCalculate $34 \cdot \begin{pmatrix} 2 & 5 \\ 4 & 1 \end{pmatrix} \cdot \begin{pmatrix} 1 & 7 \\ 3 & 0 \end{pmatrix}$ .

Assumptions1. We are given twox matrices. . We are asked to find the product of these matrices.
3. We are also given a scalar multiple of34.
4. Matrix multiplication is associative, meaning that the order in which the matrices are multiplied does not change the result.

Now, plug in the given values for the matrices to calculate the product.
$\left[\begin{array}{cc}2 &5 \\ &1\end{array}\right] \cdot \left[\begin{array}{cc}1 &7 \\3 &0\end{array}\right]$

Calculate the product of the two matrices.
$\left[\begin{array}{cc}21 +3 &27 +0 \\41 +13 &47 +10\end{array}\right]$

implify the matrix multiplication.
$\left[\begin{array}{cc}17 &14 \\7 &28\end{array}\right]$

Now that we have the product of the two matrices, we can multiply this by the scalar multiple of34.
$34 \cdot \left[\begin{array}{cc}17 &14 \\ &28\end{array}\right]$

Calculate the product of the scalar multiple and the matrix.
$\left[\begin{array}{cc}3417 &3414 \\347 &3428\end{array}\right]$