Question Bank • QB_PARAMETRIC_EM_MAT_127MCQ • 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 $\det(A) = 129$. The determinant of the scalar multiplied matrix $128A$ is: (Variation QB_PARAMETRIC_EM_MAT_127)
Options:
(A) 270532608
(B) 16512
(C) 2113536
(D) 34628173824
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 $n = 3$, $k = 128$, and $\det(A) = 129$:
$\det(128A) = 128^3 \times 129 = 2097152 \times 129 = 270532608$
Hence, the correct determinant value is $270532608$.