Allied & ICAR Exam Bank • ALLIED_2605 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Matrices and determinants

Question Statement:

An upper triangular matrix $U$ has diagonal entries $2, -1, 5, 3$. The determinant of $U^3$ is:

Options:

  • (A) -27000
  • (B) 27000
  • (C) -900
  • (D) 900

Answer Key:

A

Step-by-Step Solution & Explanation

The determinant of a triangular matrix is the product of its diagonal entries: $\det(U) = 2 \times (-1) \times 5 \times 3 = -30$. Then $\det(U^3) = (\det(U))^3 = (-30)^3 = -27000$.
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