GATE AG 2025 • Q12 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

If the matrix $\begin{bmatrix} x & -3 \\ 2 & x-5 \end{bmatrix}$ is singular, find the sum of the values of $x$.

Options:

  • (A) 5
  • (B) 6
  • (C) 0
  • (D) -1

Official Answer Key:

A

Step-by-Step Solution & Explanation

Singular ⇒ determinant = 0: x(x−5) − (−3)(2) = 0 ⇒ x² − 5x + 6 = 0 ⇒ x = 2, 3. Sum of roots = −(−5)/1 = 5.

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