Question

If $A=\left[\begin{array}{cc}-1& 2\\ 3& 4\end{array}\right]$ and $B=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]$, $2A+B+X=0$, then the matrix $X$ is

• A. $\left[\begin{array}{cc}1& 2\\ 7& 13\end{array}\right]$
• B. $\left[\begin{array}{cc}-1& 2\\ 7& -13\end{array}\right]$
• C. $\left[\begin{array}{cc}-1& -2\\ 7& 13\end{array}\right]$
• D. $\left[\begin{array}{cc}-1& -2\\ -7& -13\end{array}\right]$

Answer 1

The correct option is D $\left[\begin{array}{cc}-1& -2\\ -7& -13\end{array}\right]$

Given

$A=\left[\begin{array}{cc}-1& 2\\ 3& 4\end{array}\right],B=\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]$

And

$2A+B+X=0$

$\Rightarrow 2\left[\begin{array}{cc}-1& 2\\ 3& 4\end{array}\right]+\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]+X=0$

$\Rightarrow \left[\begin{array}{cc}-2& 4\\ 6& 8\end{array}\right]+\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]+X=0$

$\Rightarrow \left[\begin{array}{cc}-2+3& 4-2\\ 6+1& 8+5\end{array}\right]+X=0$

$\Rightarrow \left[\begin{array}{cc}1& 2\\ 7& 13\end{array}\right]+X=0$

$\therefore X=\left[\begin{array}{cc}-1& -2\\ -7& -13\end{array}\right]$