A=−1234 and  B=3−215,2A+B+X=0, then the matrix  ‘X’ is

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

1. A

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

2. B

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

3. C

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

4. D

None of these

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### Solution:

$\begin{array}{l}2A+B+X=0\\ 2\left[\begin{array}{cc}-1& 2\\ 3& 4\end{array}\right]+\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]+X=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]\\ ⇒\left[\begin{array}{cc}-2& 4\\ 6& 8\end{array}\right]+\left[\begin{array}{cc}3& -2\\ 1& 5\end{array}\right]+X=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]\\ ⇒\left[\begin{array}{cc}1& 2\\ 7& 13\end{array}\right]+X=\left[\begin{array}{cc}0& 0\\ 0& 0\end{array}\right]\\ ⇒X=\left[\begin{array}{cc}-1& -2\\ -1& -13\end{array}\right]\end{array}$

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