4. True or False? If true, prove. If false, provide a counterexample.a. If same size matrices A and B have exactly the same eigenvalues (including multiplicities), theymust be similar.b. If a square matrix A is diagonalizable, so is Ak, for any positive integer k.C.If a square invertible matrix A is diagonalizable, so is A-¹.d. If a square matrix A is invertible, then it's diagonalizable.e. For any m x n matrix A, the matrix AT A is orthogonally diagonalizable.f.Let A be a symmetric n x n matrix. Suppose ₁ and ₂ are eigenvectors corresponding to twodistinct eigenvalues of A. Then, ||x₁ + x₂ || = ||X₁|| + ||x₂||.g.If an n x n matrix A has only real eigenvalues, then it must be symmetric.

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Answered: 4. True or False? If true, prove. If…

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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