Allied & ICAR Exam Bank • ALLIED_2611 NAT • 2 Marks

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Linear and orthogonal transformations

Question Statement:

Let $P$ be an orthogonal matrix representing a reflection in $\mathbb{R}^3$. The determinant $\det(P)$ is:

Answer Key:

-1

Step-by-Step Solution & Explanation

A pure reflection reverses orientation in Euclidean space, giving determinant $\det(P) = -1$.
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