Allied & ICAR Exam Bank • ALLIED_2620 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Eigen values and Eigen vectors

Question Statement:

The sum and product of the eigenvalues of the matrix $M = \begin{bmatrix} 3 & -1 & 2 \\ 0 & 5 & 4 \\ 0 & 0 & -2 \end{bmatrix}$ are respectively:

Options:

  • (A) $6$ and $-30$
  • (B) $6$ and $30$
  • (C) $8$ and $-30$
  • (D) $10$ and $-15$

Answer Key:

A

Step-by-Step Solution & Explanation

Since $M$ is upper triangular, its eigenvalues are the diagonal entries: $3, 5, -2$. Sum = $3 + 5 - 2 = 6 = \text{trace}(M)$. Product = $3 \times 5 \times (-2) = -30 = \det(M)$.
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