Question Bank • QB_PARAMETRIC_EM_MAT_133MCQ • 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 $\det(A) = 135$. The determinant of the scalar multiplied matrix $134A$ is: (Variation QB_PARAMETRIC_EM_MAT_133)
Options:
(A) 324824040
(B) 18090
(C) 2424060
(D) 43526421360
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 $n = 3$, $k = 134$, and $\det(A) = 135$:
$\det(134A) = 134^3 \times 135 = 2406104 \times 135 = 324824040$
Hence, the correct determinant value is $324824040$.