Allied & ICAR Exam Bank • ALLIED_0773 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

If a real square matrix $A$ is skew-symmetric ($A^T = -A$), then all of its eigenvalues are:

Options:

  • (A) Either zero or purely imaginary
  • (B) Strictly positive real numbers
  • (C) Strictly negative real numbers
  • (D) Always equal to +1 or -1

Answer Key:

A

Step-by-Step Solution & Explanation

Skew-symmetric real matrices have purely imaginary eigenvalues (pairs of $\pm i\beta$) or zero.
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