**Toolbox:**

- The sum / difference $A(+/-)B$ of two $m$-by-$n$ matrices $A$ and $B$ is calculated entrywise: $(A (+/-) B)_{i,j} = A_{i,j} +/- B_{i,j}$ where 1 ≤ i ≤ m and 1 ≤ j ≤ n.

(ii)$2X-3Y$

Given

$X=\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}$

$Y=\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$

Replace the value of X and Y in the below equation.

$2X-3Y=2\begin{bmatrix}3 & 1 & 1\\5 & 2 & 3\end{bmatrix}-3\begin{bmatrix}2 & 1 & 1\\7 & 2 & 4\end{bmatrix}$

$\;\;\;\quad=\begin{bmatrix}6 & 2& 2\\10 & 4 & 6\end{bmatrix}+(-1)\begin{bmatrix}6 & 3 & 3\\21 & 6 & 12\end{bmatrix}$

$\;\;\;\quad=\begin{bmatrix}6 & 2& 2\\10 & 4 & 6\end{bmatrix}+\begin{bmatrix}-6 & -3 & -3\\-21 &- 6 & -12\end{bmatrix}$

$\;\;\;\quad=\begin{bmatrix}6-6 & 2-3& 2-3\\10-21 & 4-6 & 6-12\end{bmatrix}$

$\;\;\;\quad=\begin{bmatrix}0 & -1& -1\\-11 & -2 & -6\end{bmatrix}$