Find the matrix X satisfying 2X+pmatrix1&2\\3&4pmatrix=pmatrix3&8\\7&2pmatrix.

$\begin{pmatrix}2&5\\5&3\end{pmatrix}$

$\begin{pmatrix}1&0\\0&1\end{pmatrix}$

GATE 2026 ES – Question 11

Mathematics Foundation · Linear Algebra · 1 mark · Multiple choice

Find the matrix $X$ satisfying $$2X+\begin{pmatrix}1&2\\3&4\end{pmatrix}=\begin{pmatrix}3&8\\7&2\end{pmatrix}.$$

$\begin{pmatrix}2&5\\5&3\end{pmatrix}$
$\begin{pmatrix}-1&3\\2&-1\end{pmatrix}$
$\begin{pmatrix}1&3\\2&-1\end{pmatrix}$
$\begin{pmatrix}1&0\\0&1\end{pmatrix}$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) $\begin{pmatrix}1&3\\2&-1\end{pmatrix}$

Explanation

Subtract the known matrix entry by entry to obtain $2X=\begin{pmatrix}2&6\\4&-2\end{pmatrix}$. Divide every entry by 2: $X=\begin{pmatrix}1&3\\2&-1\end{pmatrix}$. Substitution recovers the original equation. Hence **C**.

GATE 2026 ES – Question 11

Explanation

More Linear Algebra questions