I am trying to solve an SVD problem. Assuming that A is a 3x4 matrix with the SVD , U and V are orthogonal matrices:

A = (u1 u2 u3) (1 0 0 0, 0 2 0 0, 0 0 0 0) (v1^T v2^T v3^T v4^T)

A = (1x3 matrix) (3x4 matrix) (4x1 matrix)

How do I go about finding the bases for the four fundamental subspaces C(A), C(A^T ), N(A), and N(A^T) of A?

Once I have that information, how do I find all solutions to the equation Ax=u_2, assuming (AV=U)?