Question

What must be the matrix X, if
$2X+\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]=\left[\begin{array}{cc}3& 8\\ 7& 2\end{array}\right]$ ?

• A. $\left[\begin{array}{cc}1& 3\\ 2& -1\end{array}\right]$
• B. $\left[\begin{array}{cc}1& -3\\ 2& -1\end{array}\right]$
• C. $\left[\begin{array}{cc}2& 6\\ 4& -2\end{array}\right]$
• D. $\left[\begin{array}{cc}2& -6\\ 4& -2\end{array}\right]$

Answer 1

Answer: (A)

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