1) Find a basis for each of the four fundamental subspaces of A. A = 2 122 0 5 -1 1 50 1 12 3 8 1

I1 Find a basis for the subspace of R³ consisting of all vectors such that 8₁-712+673 = 0. Hint: Notice that this single equation counts as a system of linear equations; find and describe the solutions. Answer:

1) Find a basis for each of the four fundamental subspaces of A. A = 2 122 0 5 -1 1 50 1 12 3 8 1

Let A = [v v vi = (1,0,0,0) V2 = (1,2,0,0) vs = (1,1,0, 0) vA = (2,1, 1,0) v = (0,1, 1,0) v v5 where %3D V5 Which vectors form a basis for the column space? And how many vectors are there in the basis of the null space? O v 3 O 2 vectors in basis null space O 3 vectors in basis of null space O v 1 O v_4 O v 2 O v_5 O 4 vectors in basis of null space O 1 vector in basis of null space