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GATE 2026 EC – Question 26

Engineering Mathematics · Linear Algebra · 1 mark · Multiple select

Consider the matrix $M=\begin{bmatrix}2&1&1\\1&3&0\\-1&a&b\end{bmatrix}$. Which of the following options is/are TRUE if $\det(M)\neq0$?

  1. $a=-\frac12$ and $b=-\frac12$
  2. $a=\frac12$ and $b=\frac12$
  3. $a=-3$ and $b=0$
  4. $a=\frac12$ and $b=-3$

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Show answer and explanation

Correct answer: (B) $a=\frac12$ and $b=\frac12$; (D) $a=\frac12$ and $b=-3$

Explanation

$\det M=2(3b)-1(b)+1(a+3)=5b+a+3$. This is 0 for (A) and (C) and nonzero for (B) (=6) and (D) (=−11.5).