If A=102−1and B=3142 a matrices C such that 2A+3B+2Cis a null matrix then ___

A
$\frac{1}{2} [\begin{matrix} 11 & 3 \\ 8 & 4 \end{matrix}]$
B
$\frac{1}{2} [\begin{matrix} - 11 & - 3 \\ - 16 & - 8 \end{matrix}]$
C
$\frac{1}{2} [\begin{matrix} 11 & 3 \\ 16 & 8 \end{matrix}]$
D
$[\begin{matrix} - 11 & - 3 \\ - 16 & - 8 \end{matrix}]$

Solution:

$\begin{array}{l} 2 A + 3 B + 2 C = 0 \\ \Rightarrow 2 C = - 2 A - 3 B \\ = - 2 [\begin{matrix} 1 & 0 \\ 2 & - 1 \end{matrix}] - 3 [\begin{matrix} 3 & 1 \\ 4 & 2 \end{matrix}] \\ = [\begin{matrix} - 2 - 9 & 0 - 3 \\ - 1 - 12 & 2 - 6 \end{matrix}] \\ = [\begin{matrix} - 11 & - 3 \\ - 16 & - 8 \end{matrix}] \\ c = [\begin{matrix} - \frac{11}{2} & - \frac{3}{2} \\ - 8 & - 4 \end{matrix}] \end{array}$

If $A = [\begin{matrix} 1 & 0 \\ 2 & - 1 \end{matrix}]$ and $B = [\begin{matrix} 3 & 1 \\ 4 & 2 \end{matrix}]$ a matrices C such that $2 A + 3 B + 2 C$ is a null matrix then ___

Solution:

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