Question Bank • QB_EM_099 NAT • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

If the eigenvalues of a $3 \times 3$ matrix $A$ are $1, -2,$ and $4$, calculate the determinant of $A$.

Answer Key:

-8

Step-by-Step Solution & Explanation

The determinant of a square matrix is the product of its eigenvalues: $\det(A) = \lambda_1 \times \lambda_2 \times \lambda_3 = 1 \times (-2) \times 4 = -8.0$
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