a. Let A be a 3x4 matrix. If dim Nul A = 2, then find the following: i. Rank A= ii. dim Col A = iii. dim Row A= iv. # of pivot columns = v. # of pivot rows = vi. Do the columns of A span R3?
b. Suppose B is a 4x4 matrix with eigenvalues 2, 3, -1 such that the eigenspace corresponding to 2 has dimension 1; the eigenspace corresponding to 3 has dimension 1; and the eigenspace corresponding to -1 has dimension 1. Determine whether B is diagonalizable. Justify your answer.