Question Bank • QB_SUB_EM_0004 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

If $A$ is a $3 \times 3$ matrix with $\det(A) = 5$, then the determinant $\det(2A)$ is equal to:

Answer Key:

40.0

Step-by-Step Solution & Explanation

For an $n \times n$ matrix, $\det(k A) = k^n \det(A)$. Here $n = 3$ and $k = 2$: $\det(2A) = 2^3 \det(A) = 8 \times 5 = 40$
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