Allied & ICAR Exam Bank • ALLIED_0774 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

A $3 \times 3$ real symmetric matrix $A$ has eigenvalues $2, 4,$ and $8$. The determinant of $A^{-1}$ is:

Answer Key:

0.015625

Step-by-Step Solution & Explanation

$\det(A) = 2 \times 4 \times 8 = 64$. Then $\det(A^{-1}) = 1 / \det(A) = 1 / 64 = 0.015625$.
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