Which of the following is FALSE? Symmetric matrices are always diagonalizable. Symmetric matrices are always invertible. Eigenvectors of a symmetric matrix which come from different eigenspaces must be orthogonal. Eigenvectors of a symmetric matrix which come from different eigenspaces must be linearly independent.

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CR: Review Exercises
Problem 64CR: a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving...
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Which of the following is FALSE?
Symmetric matrices are always diagonalizable.
Symmetric matrices are always invertible.
Eigenvectors of a symmetric matrix which come from different eigenspaces must be
orthogonal.
Eigenvectors of a symmetric matrix which come from different eigenspaces must be
linearly independent.
Transcribed Image Text:Which of the following is FALSE? Symmetric matrices are always diagonalizable. Symmetric matrices are always invertible. Eigenvectors of a symmetric matrix which come from different eigenspaces must be orthogonal. Eigenvectors of a symmetric matrix which come from different eigenspaces must be linearly independent.
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