Consider the following matrix. -1 0 -1 0 -1 0 -1 A = -1 0 -1 0 -1 1 1 0 -1 0 -1 Use this list of theorems to answer the following questions. (a) Is A symmetric? Explain. O Yes, because A = AT. Yes, because A # AT. O No, because A = AT. O No, because A # AT. (b) Is A diagonalizable? Explain. (Select all that apply.) O yes, by the Real Spectral Theorem O yes, by the Property of Symmetric Matrices yes, by the Fundamental Theorem of Symmetric Matrices no, by the Real Spectral Theorem no, by the Property of Symmetric Matrices no, by the Fundamental Theorem of Symmetric Matrices (c) Are the eigenvalues of A real? Explain. (Select all that apply.) O yes, by the Real Spectral Theorem yes, by the Property of Symmetric Matrices yes, by the Fundamental Theorem of Symmetric Matrices O no, by the Real Spectral Theorem no, by the Property of Symmetric Matrices O no, by the Fundamental Theorem of Symmetric Matrices
Consider the following matrix. -1 0 -1 0 -1 0 -1 A = -1 0 -1 0 -1 1 1 0 -1 0 -1 Use this list of theorems to answer the following questions. (a) Is A symmetric? Explain. O Yes, because A = AT. Yes, because A # AT. O No, because A = AT. O No, because A # AT. (b) Is A diagonalizable? Explain. (Select all that apply.) O yes, by the Real Spectral Theorem O yes, by the Property of Symmetric Matrices yes, by the Fundamental Theorem of Symmetric Matrices no, by the Real Spectral Theorem no, by the Property of Symmetric Matrices no, by the Fundamental Theorem of Symmetric Matrices (c) Are the eigenvalues of A real? Explain. (Select all that apply.) O yes, by the Real Spectral Theorem yes, by the Property of Symmetric Matrices yes, by the Fundamental Theorem of Symmetric Matrices O no, by the Real Spectral Theorem no, by the Property of Symmetric Matrices O no, by the Fundamental Theorem of Symmetric Matrices
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter4: Eigenvalues And Eigenvectors
Section4.4: Similarity And Diagonalization
Problem 40EQ
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