MAT 242 Written Homework #4 5.1, 5.2, 5.A Due: November 10 Solve the following problems, showing any necessary work. 0 -1 1. [3 points] For the matrix A = -2 0 -2 2 -4 0 -4 4 2 find a basis for the null space of A, a basis for the 3 0 3-3-1 row space of A, a basis for the column space of A, the rank of A, and the nullity of A. -5 10 -207 2. [1 point] Find the eigenvalues of the matrix A = -10 10 You do not need to state their -5 5 multiplicities. -2 6 -24 3. The eigenvalues of the matrix A = 4 16 -72 are -2 (with multiplicity 2) and -4 (with multi- 1 5 -22 plicity 1). (You do not need to find these.) Do the following for the matrix A: a. [1 point] Find a basis for the eigenspace of each eigenvalue, indicating which basis corresponds with which eigenvalue. b. [1 point] Is the matrix A diagonalizable? If so, find matrices D and P such that A = PDP- and D is a diagonal matrix. If A is not diagonalizable explain carefully why it is not diagonalizable