Please complete the following four questions, which require detailed steps.

(1) Find the nullspace of the matrix A = 2 -1 3 4 20 31 (2) Consider the matrix A = 6 -5 -6 -11 -16 (a) Find a basis for the column space (b) Find the rank of the matrix (3) Find the coordinate matrix of a = (12, 6) in R" relative to the basis B' = {(4, 0), (3, 0) } (4) Find the transition matrix from B = {(-1, 0, 0), (0, 1, 0), (0,0, -1)} and B' = {(0, 0, 2), (1, 4, 0), (5, 0, 2) }