Question: (3) Find a matrix C that has an eigenvector with eigenvalue 5, and an eigenvector with eigenvalue 3. (4) The characteristic polynomial of the matrix

(3) Find a matrix C that has an eigenvector with eigenvalue 5, and an eigenvector with eigenvalue 3. (4) The characteristic polynomial of the matrix CO M = 1 9 6 is (X - 10)(X - 10) () + 8). Find an orthonormal eigenbasis for M. (5) (a) Construct a matrix with characteristic polynomial 1 + 21 + 1 that has an eigenbasis. (b) Construct a matrix with characteristic polynomial 12 + 21 + 1 that does not have an eigenbasis

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