The GATE Grind

GATE 2026 CH – Question 23

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 1 mark · Multiple choice

Which one of the following is the pair of eigenvalues of the matrix $\begin{bmatrix} -3 & 4 \\ 4 & 3 \end{bmatrix}$ ?

  1. −7, 7
  2. −5, 5
  3. −4, 3
  4. −3, 4

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) −5, 5

Explanation

The trace is $-3 + 3 = 0$ and the determinant is $-9 - 16 = -25$. The eigenvalues satisfy $\lambda^2 - 25 = 0$, so $\lambda = \pm 5$.