The GATE Grind

GATE 2021 MT – Question 11

Engineering Mathematics · Linear algebra and matrices · 1 mark · Multiple choice

The eigenvalues of $\begin{bmatrix}1&0&-1\\0&1&0\\-1&0&1\end{bmatrix}$ are ______.

  1. 0, 2, 2
  2. 1, 1, 2
  3. 0, 1, 2
  4. 0, 1, 3

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (C) 0, 1, 2

Explanation

The middle coordinate is an eigenvector with eigenvalue 1. The remaining block [[1,−1],[−1,1]] has eigenvalues 0 and 2 from its sum and difference vectors.

Thus the full spectrum is **0,1,2, C**.