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Matrices, Eigenvalues and Eigenvectors

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Let M=[(4 -1 -9 -5), (3 -2 -5 -3), (3 0 -7 -3), (0 -1 1 -1)]

i) Show that the column vector [7,5,3,2]^T is an eigenvector for M.
ii) Find the eigenvalues for M.
iii) Determine whether or not M is diagonalisable over R, justifying your assertion and showing any necessary calculations in full.

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This solution evaluates as diagonalizable or not.

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