Allied & ICAR Exam Bank • ALLIED_0019 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Linear and orthogonal transformations

Question Statement:

Which of the following matrices is symmetric?

Options:

  • (A) $\begin{pmatrix} 1 & 5 \\ 5 & 2 \end{pmatrix}$
  • (B) $\begin{pmatrix} 0 & 5 \\ -5 & 0 \end{pmatrix}$
  • (C) $\begin{pmatrix} 1 & 2 \\ 3 & 4 \end{pmatrix}$
  • (D) $\begin{pmatrix} 1 & 0 \\ 2 & 1 \end{pmatrix}$

Answer Key:

A

Step-by-Step Solution & Explanation

A matrix is symmetric when $A = A^T$, which holds for $\begin{pmatrix} 1 & 5 \\ 5 & 2 \end{pmatrix}$.
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