Question

What must be the matrix X, if
$2X + \begin{bmatrix}1&2\\ 3&4\end{bmatrix} = \begin{bmatrix}3&8\\ 7&2\end{bmatrix}$ ?

• A. $\begin{bmatrix}1&3\\ 2&-1\end{bmatrix}$
• B. $\begin{bmatrix}1& -3\\ 2&-1\end{bmatrix}$
• C. $\begin{bmatrix} 2&6\\ 4 &-2\end{bmatrix}$
• D. $\begin{bmatrix}2 &-6 \\ 4&-2\end{bmatrix}$

Answer 1

Answer: (A)

Here
$2X = \begin{bmatrix}3&8\\ 7&2\end{bmatrix}_{2\times2} -\begin{bmatrix}1&2\\ 3&4\end{bmatrix}_{2\times2} $
Note: The two matrices can only be added or subtracted iff (if and only if) they are of same order.
$\therefore \ 2X = \begin{bmatrix}2& 6\\ 4& -2\end{bmatrix} $
Thus, $X = \begin{bmatrix} 1&3\\ 2& -1 \end{bmatrix}$