GATE ES 2021 | Question: 26

Question

The $2 \times 2$ matrices $P$ and $Q$ satisfy the following relations:
$\mathbf{P}+\mathbf{Q}=\left[\begin{array}{cc}3 & 1 \\ 2 & 12\end{array}\right]$ and
$\mathbf{P}-\mathbf{Q}=\left[\begin{array}{cc}-1 & -7\\ 8 & 2\end{array}\right]$

The matrix $Q$ is equal to

• A. $\left[\begin{array}{II}2 & 4 \\ -3 & 5\end{array}\right]$
• B. $\left[\begin{array}{II}1 & -3 \\ 5 & 7\end{array}\right]$
• C. $\left[\begin{array}{II}2 & -3 \\ 4 & 5\end{array}\right]$
• D. $\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]$

 

Answer 1

Subtracting relation 2 from relation 1:

$\mathbf{P}+\mathbf{Q}-(\mathbf{P}-\mathbf{Q}) = $ $\left[\begin{array}{cc}3+1 & 1+7 \\ 2-8 & 12-2\end{array}\right]$

2*$\mathbf{Q} =$ $\left[\begin{array}{cc}4 & 8 \\ -6 & 10\end{array}\right]$

$\mathbf{Q} = \left[\begin{array}{cc}2 & 4 \\ -3 & 5\end{array}\right]$

Hence, right answer is A.