Question Bank • QB_PARAMETRIC_EM_MAT_106MCQ • 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 $\det(A) = 108$. The determinant of the scalar multiplied matrix $107A$ is: (Variation QB_PARAMETRIC_EM_MAT_106)
Options:
(A) 132304644
(B) 11556
(C) 1236492
(D) 14156596908
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 $n = 3$, $k = 107$, and $\det(A) = 108$:
$\det(107A) = 107^3 \times 108 = 1225043 \times 108 = 132304644$
Hence, the correct determinant value is $132304644$.