Find 3A-2B.

cofak48
2022-08-04
Answered

Let $A=\left[\begin{array}{cc}3& 2\\ 5& 3\end{array}\right]$ and $B=\left[\begin{array}{cc}-7& 9\\ 1& -9\end{array}\right]$

Find 3A-2B.

Find 3A-2B.

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Barbara Klein

Answered 2022-08-05
Author has **19** answers

$3A-2B=3\left(\begin{array}{cc}3& 2\\ 5& 3\end{array}\right)-2\left(\begin{array}{cc}-7& 9\\ 1& -9\end{array}\right)$

$=\left(\begin{array}{cc}9& 6\\ 15& 9\end{array}\right)-\left(\begin{array}{cc}-14& 18\\ 2& -18\end{array}\right)$

$=\left(\begin{array}{cc}23& -12\\ 13& 27\end{array}\right)$

$=\left(\begin{array}{cc}9& 6\\ 15& 9\end{array}\right)-\left(\begin{array}{cc}-14& 18\\ 2& -18\end{array}\right)$

$=\left(\begin{array}{cc}23& -12\\ 13& 27\end{array}\right)$

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T:${M}_{22}$

$\left(\left[\begin{array}{cc}{x}_{11}& {x}_{12}\\ {x}_{21}& {x}_{22}\end{array}\right]\right)=\left[\begin{array}{cc}{x}_{12}-5{x}_{21}-{x}_{22}& -{x}_{11}-2{x}_{12}+3{x}_{21}+4{x}_{22}\\ -3{x}_{21}& -{x}_{11}-{x}_{12}+{x}_{21}+3{x}_{22}\end{array}\right]$

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Is it:

$\left[\begin{array}{cccc}0& 1& -5& -1\\ -1& -2& 3& 4\\ 0& 0& -3& 0\\ -1& -1& 1& 3\end{array}\right]$

If so, how could this be multiplied by a 2x2 matrix to give another 2x2 matrix. (2x2 matrices cannot multiply with 4x4 matrices).

T:${M}_{22}$

$\left(\left[\begin{array}{cc}{x}_{11}& {x}_{12}\\ {x}_{21}& {x}_{22}\end{array}\right]\right)=\left[\begin{array}{cc}{x}_{12}-5{x}_{21}-{x}_{22}& -{x}_{11}-2{x}_{12}+3{x}_{21}+4{x}_{22}\\ -3{x}_{21}& -{x}_{11}-{x}_{12}+{x}_{21}+3{x}_{22}\end{array}\right]$

What is the matrix that represents this ${M}_{22}$->${M}_{22}$ transformation?

Is it:

$\left[\begin{array}{cccc}0& 1& -5& -1\\ -1& -2& 3& 4\\ 0& 0& -3& 0\\ -1& -1& 1& 3\end{array}\right]$

If so, how could this be multiplied by a 2x2 matrix to give another 2x2 matrix. (2x2 matrices cannot multiply with 4x4 matrices).

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How to do this question in regards of matrices and transformation?