prove no.2 VII. Prove the following statements.1. Let B be an orthonormal basis of a finite-dimensional inner product space V. Suppose that thea1a2coordinate vector [v]B =Then |v|a₁|²+|a₂|² +·+|an|².2. If A is similar to a diagonal matrix D then A is similar to AT.3. Let A be an n x n matrix with eigenvalues A₁ and A2, where A₁ A2. If Sx, is the eigenspaceassociated with Ai, i = 1,2, then Sx₁ Sx₂ = {0}.

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Answered: [an] 2. If A is similar to a diagonal…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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[an] 2. If A is similar to a diagonal matrix D then A is similar to AT.