Allied & ICAR Exam Bank • ALLIED_0775 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Positive definite matrices

Question Statement:

According to Sylvester's criterion, a real symmetric matrix $A$ is positive definite if and only if:

Options:

  • (A) All of its leading principal minors are strictly positive
  • (B) All of its diagonal entries are zero
  • (C) Its determinant is negative
  • (D) Its trace is negative

Answer Key:

A

Step-by-Step Solution & Explanation

Sylvester's criterion requires that all leading principal minors $\Delta_1, \Delta_2, \dots, \Delta_n > 0$ for positive definiteness.
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