Find the eigenvalues and eigenvectors of the following matrices. (Use the
Chapter 8, Problem 8.1.9(choose chapter or problem)
Show that the inverse \(A^{-1}\) exists if and only if none of the eigenvalues \(\lambda_{1}, \cdots, \lambda_{n}\) of A is zero, and then \(A^{-1}\) has the eigenvalues \(1 / \lambda_{1}, \cdots, 1 / \lambda_{n}\).
Text Transcription:
A^-1
lambda_1, cdots, lambda_n
1/lambda_1, cdots, 1/lambda_n
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