A) \[\left[ \begin{align} & \begin{matrix} 8 & -1 & 2 \\ \end{matrix} \\ & \begin{matrix} -1 & 10 & -1 \\ \end{matrix} \\ \end{align} \right]\]
B) \[\left[ \begin{align} & \begin{matrix} 8 & -1 & 2 \\ \end{matrix} \\ & \begin{matrix} -1 & 10 & -1 \\ \end{matrix} \\ \end{align} \right]\]
C) \[\left[ \begin{align} & \begin{matrix} 8 & 1 & -2 \\ \end{matrix} \\ & \begin{matrix} -1 & 10 & -1 \\ \end{matrix} \\ \end{align} \right]\]
D) \[\left[ \begin{align} & \begin{matrix} 8 & 1 & 1 \\ \end{matrix} \\ & \begin{matrix} 1 & 10 & 1 \\ \end{matrix} \\ \end{align} \right]\]
Correct Answer: B
Solution :
We have \[2A+3B=\left[ \begin{matrix} 2 & -1 & 4 \\ 3 & 2 & 5 \\ \end{matrix} \right]\] ?..(i) and \[A+2B=\left[ \begin{matrix} 5 & 0 & 3 \\ 1 & 6 & 2 \\ \end{matrix} \right]\] .....(ii) Multiply Eq. (ii) by 2 and subtracting Eq. (i) from (ii), we get \[B=2\left[ \begin{matrix} 5 & 0 & 3 \\ 1 & 6 & 2 \\ \end{matrix} \right]-\left[ \begin{matrix} 2 & -1 & 4 \\ 3 & 2 & 5 \\ \end{matrix} \right]\] \[=\left[ \begin{matrix} 8 & 1 & 2 \\ -1 & 10 & -1 \\ \end{matrix} \right]\]
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