Question: (3) (10 marks) Consider matrix A = -2 2 1 (a) (2 mark) Find the characteristic polynomial of matrix A. (b) (1 mark) Find eigenvalues

(3) (10 marks) Consider matrix A = -2 2 1 (a) (2 mark) Find the characteristic polynomial of matrix A. (b) (1 mark) Find eigenvalues of the matrix A. (c) (2 mark) Find a basis for the eigenspaces of matrix A.(d) (1 mark) What is the algebraic and geometric multiplicities of its eigenvalues. (e) (2 mark) Show that the matrix is diagonalizable and find an invertible matrix P and a diagonal matrix D such that P-1AP = D (f) (2 mark) Find a formula for An

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