Q.Find x, y, z if $\left\{3\begin{bmatrix}2&0\\0&2\\2&2\end{bmatrix}-4\begin{bmatrix}1&1\\-1&2\\3&1\end{bmatrix}\right\}\begin{bmatrix}1\\2\end{bmatrix}=\begin{bmatrix}x-3\\y-1\\2z\end{bmatrix}$.

Given $\left\{3\begin{bmatrix}2&0\\0&2\\2&2\end{bmatrix}-4\begin{bmatrix}1&1\\-1&2\\3&1\end{bmatrix}\right\}\begin{bmatrix}1\\2\end{bmatrix}=\begin{bmatrix}x-3\\y-1\\2z\end{bmatrix}$.

Step 1 — scale each matrix:

$3\begin{bmatrix}2&0\\0&2\\2&2\end{bmatrix}=\begin{bmatrix}6&0\\0&6\\6&6\end{bmatrix}$, $4\begin{bmatrix}1&1\\-1&2\\3&1\end{bmatrix}=\begin{bmatrix}4&4\\-4&8\\12&4\end{bmatrix}$

Step 2 — subtract:

$\begin{bmatrix}6-4&0-4\\0-(-4)&6-8\\6-12&6-4\end{bmatrix}=\begin{bmatrix}2&-4\\4&-2\\-6&2\end{bmatrix}$

Step 3 — multiply by $\begin{bmatrix}1\\2\end{bmatrix}$:

Row 1: $2(1)+(-4)(2)=2-8=-6$ …

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