GATE EE 2024 Set 1 — Question 32
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Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
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Question
The sum of the eigenvalues of the matrix is ______ (rounded off to the nearest integer).
Correct answer
29 to 29
Solution
Let . Let the eigenvalues of be and .
The sum of the eigenvalues of is given by the trace:The product of the eigenvalues of is given by the determinant:The matrix . The eigenvalues of are and .
The sum of the eigenvalues of is:
The sum of the eigenvalues of is given by the trace:The product of the eigenvalues of is given by the determinant:The matrix . The eigenvalues of are and .
The sum of the eigenvalues of is:
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