The GATE Grind

GATE 2023 CH – Question 47

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors · 2 marks · Numerical answer

If a matrix $M$ is defined as $M = \begin{bmatrix} 10 & 6 \\ 6 & 10 \end{bmatrix}$, the sum of all the eigenvalues of $M^3$ is equal to __________ (in integer).

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: 4160

Explanation

The eigenvalues of $M$ are $10 \pm 6$, that is 16 and 4. The eigenvalues of $M^3$ are their cubes, $4096$ and $64$, so the sum is $4160$.