Question Bank • QB_PARAMETRIC_EM_MAT_118MCQ • 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 $\det(A) = 120$. The determinant of the scalar multiplied matrix $119A$ is: (Variation QB_PARAMETRIC_EM_MAT_118)
Options:
(A) 202219080
(B) 14280
(C) 1699320
(D) 24064070520
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 $n = 3$, $k = 119$, and $\det(A) = 120$:
$\det(119A) = 119^3 \times 120 = 1685159 \times 120 = 202219080$
Hence, the correct determinant value is $202219080$.