IIT JAM 2022 Question 41: Vector spaces, rank and eigenvalues

The sum of the eigenvalues of the square matrix $\begin{pmatrix} 1 & 1 & 3 \\ 1 & 5 & 1 \\ 3 & 1 & 1 \end{pmatrix}$ is _______ (in integer).

Answer and worked solution

Answer: 7 to 7

The sum of the eigenvalues of a square matrix equals its trace, the sum of the diagonal entries.

Here the trace is $1 + 5 + 1 = 7$ . The answer is $7$ .

Plain-text version

The sum of the eigenvalues of the square matrix [1 1 3; 1 5 1; 3 1 1] is _ (in integer).

Vector spaces, rank and eigenvalues has come up 41 times in 6 exams since 2008.

This question is on Eigenvalues and eigenvectors, part of Vector spaces, rank and eigenvalues in Mathematics.

The scalars and directions a matrix only stretches, and what they say about invertibility and trace.

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