Question

If $X+Y=\left[ \begin{matrix} 7 & 0 \\\ 2 & 5 \\\ \end{matrix} \right]$ and $X-Y=\left[ \begin{matrix} 3 & 0 \\\ 0 & 3 \\\ \end{matrix} \right]$ , then X is equal to

• 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. $\left[ \begin{matrix} 7 & 1 \\\ 0 & 4 \\\ \end{matrix} \right]$

Answer 1

Answer: (C)

$\left[ \begin{matrix} 5 & 0 \\\ 1 & 4 \\\ \end{matrix} \right]$

Answer 2

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
$2X=\left[ \begin{matrix} 7 & 0 \\\ 2 & 5 \\\ \end{matrix} \right]+\left[ \begin{matrix} 3 & 0 \\\ 0 & 3 \\\ \end{matrix} \right]=\left[ \begin{matrix} 10 & 0 \\\ 2 & 8 \\\ \end{matrix} \right]$
$\Rightarrow$ $X=\left[ \begin{matrix} 5 & 0 \\\ 1 & 4 \\\ \end{matrix} \right]$