Solve the following problems, showing any necessary work. 8 24 12 Let A = 0 4 U 6 12 10 (a) [4 points] Find the eigenvalues of the matrix A. (b) [6 points] Find a basis for the eigenspace of each eigenvalue, indicating which basis cor- responds with which eigenvalue. (c) [6 points] Is the matrix A diagonalizable? If so, nd matrices D and P such that A = PUP1 and D is a diagonal matrix. If A is not diagonalizable explain carefully why it is not diagonalizable