Question Bank • QB_PARAMETRIC_EM_MAT_103MCQ • 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 $\det(A) = 105$. The determinant of the scalar multiplied matrix $104A$ is: (Variation QB_PARAMETRIC_EM_MAT_103)
Options:
(A) 118110720
(B) 10920
(C) 1135680
(D) 12283514880
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 $n = 3$, $k = 104$, and $\det(A) = 105$:
$\det(104A) = 104^3 \times 105 = 1124864 \times 105 = 118110720$
Hence, the correct determinant value is $118110720$.