Given a matrix,What would be the sum of eigenvalues ofAandndash;1? (Give the answer upto 3 decimal places )Correct answer is '1.125'. Can you explain this answer?

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Given a matrix,

What would be the sum of eigenvalues of A^–1? (Give the answer upto 3 decimal places )

Correct answer is '1.125'. Can you explain this answer?

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Linear Algebra NAT Level - 1

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Given a matrix,What would be the sum of eigenvalues ofA–1? (Give...

The characteristic equation of A is,

∴ the characteristic root of A are given by

λ = 2, 2, 8

We know that if

are the eigenvalues of A, then

will be the eigenvalues of A^–1.

Hence, in this case, eigenvalues of A^–1 will be

∴ Sum of eigenvalues of

The correct answer is: 1.125

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Given a matrix,What would be the sum of eigenvalues ofA–1? (Give the answer upto 3 decimal places )Correct answer is '1.125'. Can you explain this answer?

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