If A is an n n matrix whose eigenvalues are all nonzero, then A is nonsingular.

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If A is an n × n matrix whose eigenvalues are all nonzero, then A is nonsingular.
In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to show that the statement is not always true.

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Linear Algebra with Applications

ISBN: 978-0131857858

7th edition

Authors: Steven J. Leon

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Question Posted: Jun 13, 2016 01:04 AM

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If A is an n n matrix whose eigenvalues are all nonzero, then A is nonsingular.

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The statement is true If A were singular then we would have det A 0I det ...View the full answer

Linear Algebra with Applications

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