5. Let A be an n x n matrix. (a) (b) Show that if A is an orthogonal matrix, then det(A) = ±1. Show that if A 0 and A³ = 0, then A is not diagonalizable. (Hint: Assume A is diagonalizable and then get a contraction.)
5. Let A be an n x n matrix. (a) (b) Show that if A is an orthogonal matrix, then det(A) = ±1. Show that if A 0 and A³ = 0, then A is not diagonalizable. (Hint: Assume A is diagonalizable and then get a contraction.)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 26CM: Find an orthogonal matrix P such that PTAP diagonalizes the symmetric matrix A=[1331].
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