GATE AG 2019 • Q12 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

The determinant of the matrix $A = \begin{bmatrix} 2 & 1 & 1 \\ 2 & 3 & 2 \\ 1 & 2 & 1 \end{bmatrix}$ is

Options:

  • (A) 1
  • (B) 0
  • (C) -1
  • (D) 2

Official Answer Key:

C

Step-by-Step Solution & Explanation

Expand along the first row: det(A) = 2(3×1 − 2×2) − 1(2×1 − 2×1) + 1(2×2 − 3×1) = 2(3−4) − 1(2−2) + 1(4−3) = 2(−1) − 0 + 1(1) = −2 + 1 = −1. Answer: (C) -1.

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