True (with reason) or false (with example). "Orthonormal" is not assumed. (a) A matrix

Chapter 6, Problem 21

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True (with reason) or false (with example). "Orthonormal" is not assumed. (a) A matrix with real eigenvalues and eigenvectors is symmetric. (b) A matrix with real eigenvalues and orthogonal eigenvectors is symmetric. (c) The inverse of a symmetric matrix is symmetric. (d) The eigenvector matrix S of a symmetric matrix is symmetric.

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