Allied & ICAR Exam Bank • ALLIED_2625 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

If all the eigenvalues of a real symmetric matrix $A$ are strictly positive, then the quadratic form $x^T A x$ is:

Options:

  • (A) Positive definite
  • (B) Negative definite
  • (C) Indefinite
  • (D) Positive semi-definite with zero minimum

Answer Key:

A

Step-by-Step Solution & Explanation

A real symmetric matrix with all positive eigenvalues is positive definite, ensuring $x^T A x > 0$ for all $x \neq 0$.
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