GATE CE 2020 Set 2 — Question 37
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Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
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Question
A matrix is given belowThe eigenvalues of are
Correct answer
(D) 1, 2, 5, 7
Solution
The matrix is a block upper triangular matrix of the form , where:
and .
The eigenvalues of are the union of the eigenvalues of and .
For : . Eigenvalues are .
For : . Eigenvalues are .
The eigenvalues of are .
and .
The eigenvalues of are the union of the eigenvalues of and .
For : . Eigenvalues are .
For : . Eigenvalues are .
The eigenvalues of are .
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