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Question: 5 consider a 3x3 matrix a such that the sum...

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(5) Consider a 3x3 matrix A such that the sum of the entries in each of its columns is one. Show that the matrix must have 1 among its eigenvalues. Further, show that if the matrix is also symmetric then (1, 1, 1) must be an eigenvector. Hint: Show that the columns of A--I, where I is the identity matrix, all lie on the same two dimensional plane, and are thus linearly dependent.

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