Wherever possible, write each of the following as a single matrix.

(i) $\begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} + \begin{bmatrix} -1 & -2 \ 1 & -7 \end{bmatrix}$

(ii) $\begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \end{bmatrix} - \begin{bmatrix} 0 & 2 & 3 \ 6 & -1 & 0 \end{bmatrix}$

(iii) $\begin{bmatrix} 0 & 1 & 2 \ 4 & 6 & 7 \end{bmatrix} + \begin{bmatrix} 3 & 4 \ 6 & 8 \end{bmatrix}$

(i) Given,

$\phantom{\Rightarrow} \begin{bmatrix} 1 & 2 \ 3 & 4 \end{bmatrix} + \begin{bmatrix} -1 & -2 \ 1 & -7 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 1 + (-1) & 2 + (-2) \ 3 + 1 & 4 + (-7) \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 0 & 0 \ 4 & -3 \end{bmatrix}.$

Hence, resultant matrix = $\begin{bmatrix} 0 & 0 \ 4 & -3 \end{bmatrix}$.

(ii) Given,

$\phantom{\Rightarrow} \begin{bmatrix} 2 & 3 & 4 \ 5 & 6 & 7 \end{bmatrix} - \begin{bmatrix} 0 & 2 & 3 \ 6 & -1 & 0 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 2 - 0 & 3 - 2 & 4 - 3 \ 5 - 6 & 6 - (-1) & 7 - 0 \end{bmatrix} \\[1em] \Rightarrow \begin{bmatrix} 2 & 1 & 1 \ -1 & 7 & 7 \end{bmatrix}.$

Hence, resultant matrix = $\begin{bmatrix} 2 & 1 & 1 \ -1 & 7 & 7 \end{bmatrix}$.

(iii) Given,

$\begin{bmatrix} 0 & 1 & 2 \ 4 & 6 & 7 \end{bmatrix} + \begin{bmatrix} 3 & 4 \ 6 & 8 \end{bmatrix}$

The above calculation is not possible because for addition the order of both matrices must be equal.