Question Bank • QB_PARAMETRIC_EM_MAT_130MCQ • 1 Mark
Section 1: Engineering Mathematics
Linear Algebra: Matrices & Determinants
Subtopic: Determinant properties
Question Statement:
Let $A$ be a $3 \times 3$ real matrix with $\det(A) = 132$. The determinant of the scalar multiplied matrix $131A$ is: (Variation QB_PARAMETRIC_EM_MAT_130)
Options:
(A) 296748012
(B) 17292
(C) 2265252
(D) 38873989572
Answer Key:
A
Step-by-Step Solution & Explanation
For any $n \times n$ square matrix $A$ and a scalar $k$, the determinant scaling property states that:
$\det(k A) = k^n \det(A)$
Given that $n = 3$, $k = 131$, and $\det(A) = 132$:
$\det(131A) = 131^3 \times 132 = 2248091 \times 132 = 296748012$
Hence, the correct determinant value is $296748012$.