GATE EC 2021 Set 1 — Question 46
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Engineering Mathematics → Linear Algebra → Eigenvalues & Eigenvectors
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Question
A real non-singular matrix with repeated eigenvalue is given aswhere is a real positive number. The value of (rounded off to one decimal place) is _________.
Correct answer
10 to 10
Solution
The characteristic equation of matrix is given by :For the matrix to have repeated eigenvalues, the discriminant of this quadratic equation must be zero:Since is given as a real positive number, .
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