Question: 1. Consider the matrix below A = 1 5 H a Find the eigenvalues and eigenvectors of the matrix. b) Show that the matrix can

1. Consider the matrix below A = 1 5 H a Find the eigenvalues and eigenvectors of the matrix. b) Show that the matrix can be written using the spectral decomposition theorem. c) Show that the matrix S formed by taking the eigenvectors as columns is orthogonal. d) Show that S" AS is a diagonal matrix with the diagonal elements being the eigen- values

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