GATE CE 2026 Set 2 — Question 11
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Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
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Question
Matrix has the eigenvalues 1, 2, and 3. The Trace of is
Correct answer
(B) 14
Solution
For any matrix , if its eigenvalues are , then the eigenvalues of are . The trace of a matrix is the sum of its eigenvalues. Given eigenvalues of are 1, 2, and 3, the eigenvalues of are , , and . Therefore, Trace() = .
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