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QUESTION 5 0 1 Consider the matrix A = 1 0 1 10 1 a) Find all eigenvalues of A. (4 marks) b) Find the eigenvector and the basis for the eigenspace corresponding to the smallest eigenvalue of A obtained in a). (7 marks) c) Given the basis for the largest eigenvalue is Show that A is diagonalizable. (2 marks) d) Find the diagonal matrix D and the invertible matrix P such that D = P- AP (if exists). (2 marks) e) Based on the obtained eigenvalues in a), i) find the trace and the determinant of A. (3 marks) ii) find all eigenvalues of A . (Hint: Do not use |A - 1/) =0) (2 marks)