GATE ME 2022 Set 2 — Question 48
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Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
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Question
If the sum and product of eigenvalues of a real matrix are 4 and respectively, then is ______ (in integer).
Correct answer
2 to 2
Solution
Let the eigenvalues be and .
Sum of eigenvalues = Trace of the matrix: .
Product of eigenvalues = Determinant of the matrix: .
Substituting into the determinant equation: .
Sum of eigenvalues = Trace of the matrix: .
Product of eigenvalues = Determinant of the matrix: .
Substituting into the determinant equation: .
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