Question Bank • QB_PARAMETRIC_EM_MAT_121MCQ • 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 $\det(A) = 123$. The determinant of the scalar multiplied matrix $122A$ is: (Variation QB_PARAMETRIC_EM_MAT_121)
Options:
(A) 223349304
(B) 15006
(C) 1830732
(D) 27248615088
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 $n = 3$, $k = 122$, and $\det(A) = 123$:
$\det(122A) = 122^3 \times 123 = 1815848 \times 123 = 223349304$
Hence, the correct determinant value is $223349304$.