Question Bank • QB_PARAMETRIC_EM_MAT_109MCQ • 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 $\det(A) = 111$. The determinant of the scalar multiplied matrix $110A$ is: (Variation QB_PARAMETRIC_EM_MAT_109)
Options:
(A) 147741000
(B) 12210
(C) 1343100
(D) 16251510000
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 $n = 3$, $k = 110$, and $\det(A) = 111$:
$\det(110A) = 110^3 \times 111 = 1331000 \times 111 = 147741000$
Hence, the correct determinant value is $147741000$.