Question Bank • QB_PARAMETRIC_EM_MAT_112MCQ • 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 $\det(A) = 114$. The determinant of the scalar multiplied matrix $113A$ is: (Variation QB_PARAMETRIC_EM_MAT_112)
Options:
(A) 164490258
(B) 12882
(C) 1455666
(D) 18587399154
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 $n = 3$, $k = 113$, and $\det(A) = 114$:
$\det(113A) = 113^3 \times 114 = 1442897 \times 114 = 164490258$
Hence, the correct determinant value is $164490258$.