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

A
$[\begin{matrix} 1 & 2 \\ 7 & 13 \end{matrix}]$
B
$[\begin{matrix} - 1 & - 2 \\ - 7 & - 13 \end{matrix}]$
C
$- [\begin{matrix} 1 & 2 \\ 7 & 13 \end{matrix}]$
D
None of these

Solution:

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

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

Solution:

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