Consider the 4x5 matrix A=

0	1	0	-2	0
0	1	1	-2	3
0	0	0	0	1
0	0	0	0	0

a) Show that v = [-1,1,0,0]^T lies in C(A), the column space of A. Is there more than one way to write v as a linear combination of the columns of A? Explain.

b) Find the basis for the null space of A and Compute dim N(A).

c) Write all solutions to the linear sustem Ax = [-1,1,0,0]^T.

d) Does the set of solutions to the equation Ax = [-1,1,0,0]^T form a subspace of R^5? Explain