A) \[\left[ \begin{matrix} 5 & 0 \\ 0 & 4 \\ \end{matrix} \right]\]
B) \[\left[ \begin{matrix} 7 & 0 \\ 1 & 5 \\ \end{matrix} \right]\]
C) \[\left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right]\]
D) \[\left[ \begin{matrix} 7 & 1 \\ 0 & 4 \\ \end{matrix} \right]\]
Correct Answer: C
Solution :
Given, \[X+Y=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right]\] ?.. (i) and \[X-Y=\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]\] ?..(ii) On adding both equation, we get \[2X=\left[ \begin{matrix} 7 & 0 \\ 2 & 5 \\ \end{matrix} \right]+\left[ \begin{matrix} 3 & 0 \\ 0 & 3 \\ \end{matrix} \right]=\left[ \begin{matrix} 10 & 0 \\ 2 & 8 \\ \end{matrix} \right]\] \[\Rightarrow \] \[X=\left[ \begin{matrix} 5 & 0 \\ 1 & 4 \\ \end{matrix} \right]\]
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