Question

If $A=\left[\begin{array}{cc}1& 2\\ -3& -6\end{array}\right]$, $B=\left[\begin{array}{cc}7& 2\\ -3& -8\end{array}\right]$, $2X+A=B$. Find $X$.

• A. $\left[\begin{array}{cc}8& 4\\ -6& -8\end{array}\right]$
• B. $\left[\begin{array}{cc}1& 2\\ -3& -6\end{array}\right]$
• C. $\left[\begin{array}{cc}6& 0\\ 0& -2\end{array}\right]$
• D. $\left[\begin{array}{cc}3& 0\\ 0& -1\end{array}\right]$

Answer 1

The correct option is D $\left[\begin{array}{cc}3& 0\\ 0& -1\end{array}\right]$

Given, $A=\left[\begin{array}{cc}1& 2\\ -3& -6\end{array}\right]B=\left[\begin{array}{cc}7& 2\\ -3& 8\end{array}\right]$ and $2X+A=B$

$\Rightarrow 2X=B-A$

$\Rightarrow 2X=\left[\begin{array}{cc}7& 2\\ -3& -8\end{array}\right]-\left[\begin{array}{cc}1& 2\\ -3& -6\end{array}\right]$

$\Rightarrow 2X=\left[\begin{array}{cc}6& 0\\ 0& -2\end{array}\right]$

$\Rightarrow X=\left[\begin{array}{cc}3& 0\\ 0& -1\end{array}\right]$

$\therefore$ Option D will be correct.