Show that A 1 exists if and only if the eigenvalues 1 , , n are all nonzero, and then A 1 has the eigenvalues 1 1 , ,1 n ...

By Theorem 1 in Sec 78 the inverse exists if and only if det A 0 On the oth ...

Show that A -1 exists if and only if the eigenvalues 1 , ,

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Show that A^-1exists if and only if the eigenvalues λ₁, · · ·, λ_n are all nonzero, and then A^-1 has the eigenvalues 1/λ₁, · · ·,1/λ_n.

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Advanced Engineering Mathematics

ISBN: 978-0470458365

10th edition

Authors: Erwin Kreyszig

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Question Posted: Nov 27, 2018 04:16 AM

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Show that A -1 exists if and only if the eigenvalues 1 , ,

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By Theorem 1 in Sec 78 the inverse exists if and only if det A 0 On the oth...View the full answer

Advanced Engineering Mathematics

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