GATE AG 2022 • Q17 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

The matrix $\begin{bmatrix} (3-x) & 2 & 2 \\ 2 & (4-x) & 1 \\ -2 & -4 & (-1-x) \end{bmatrix}$ is singular for the following values of $x$:

Options:

  • (A) $x = 0$ and $x = 3$
  • (B) $x = 0$ and $x = -3$
  • (C) $x = 0$ and $x = 6$
  • (D) $x = 0$ and $x = -6$

Official Answer Key:

A

Step-by-Step Solution & Explanation

• Expanding det along row 1: det = (3−x)(x²−3x) + 4x − 4x = −x³+6x²−9x = −x(x−3)² • Setting det=0: x=0 or x=3 (repeated root).

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test