Allied & ICAR Exam Bank • ALLIED_0001 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

The eigenvalues of a $2 \times 2$ real symmetric matrix $A$ are $3$ and $7$. The trace and determinant of the matrix $A$ are respectively:

Options:

  • (A) 10 and 21
  • (B) 21 and 10
  • (C) 4 and 21
  • (D) 10 and 4

Answer Key:

A

Step-by-Step Solution & Explanation

For any square matrix, $\text{Trace}(A) = 3 + 7 = 10$, and $\det(A) = 3 \times 7 = 21$.
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