Question

I need help with this problem

Answer 1

`a)\begin{pmatrix}44 & 22 \\ -14 & -7\end{pmatrix}\:b)\:\begin{pmatrix}6 & -2 \\ 3 & -1\end{pmatrix}\:c)\:\begin{pmatrix}4 & -7 \\ -1 & -7\end{pmatrix}`

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2) So, let's begin with the lower-left product of matrices:

`\begin{gathered} \begin{pmatrix}-2 & 12 \\ -1 & -3\end{pmatrix}*\begin{pmatrix}2 & 1 \\ 4 & 2\end{pmatrix}= \\ \begin{pmatrix}\left(-2\right)\cdot \:2+12\cdot \:4&\left(-2\right)\cdot \:1+12\cdot \:2\\ \left(-1\right)\cdot \:2+\left(-3\right)\cdot \:4&\left(-1\right)\cdot \:1+\left(-3\right)\cdot \:2\end{pmatrix} \\ \begin{pmatrix}44&22\\ -14&-7\end{pmatrix} \end{gathered}`

Now for the next pair of matrices in the middle:

`\begin{gathered} \begin{pmatrix}2 & 0 \\ 1 & 0\end{pmatrix}*\begin{pmatrix}3 & -1 \\ 2 & 2\end{pmatrix}= \\ \begin{pmatrix}2\cdot \:3+0\cdot \:2&2\left(-1\right)+0\cdot \:2\\ 1\cdot \:3+0\cdot \:2&1\cdot \left(-1\right)+0\cdot \:2\end{pmatrix} \\ \begin{pmatrix}6&-2\\ 3&-1\end{pmatrix} \end{gathered}`

Notice that each row is multiplied by each correspondent column.

And finally, the pair on the lower-right:

`\begin{gathered} \begin{pmatrix}5&-2\\ \:\:\:4\:&-3\end{pmatrix}* \begin{pmatrix}2&-1\\ \:\:3&1\end{pmatrix} \\ \begin{pmatrix}5\cdot \:2+\left(-2\right)\cdot \:3&5\left(-1\right)+\left(-2\right)\cdot \:1\\ 4\cdot \:2+\left(-3\right)\cdot \:3&4\left(-1\right)+\left(-3\right)\cdot \:1\end{pmatrix} \\ \begin{pmatrix}4&-7\\ -1&-7\end{pmatrix} \end{gathered}`

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