1. The problem statement, all variables and given/known data Let x [itex]\in[/itex] RN, y [itex]\in[/itex] RM & A [itex]\in[/itex] RMxN be a matrix. Denote the columns of A by Ak, k = 1,...,N. Let R(A) & N(A) be the range & null space of A respectively. a) How do the colmuns of A relate to the range of A? b) Your task is to find the solution to the problem y = Ax, where y & A are known & M = N. What role do R(A) & N(A) play? c) Let RN [itex]\ni[/itex] x = (x1,x2), x1 [itex]\in[/itex] RN1, x2 [itex]\in[/itex] RN2 & N1 + N2 = N. Let A [itex]\in[/itex] RN1xN & consider the problem Ax = 0. Assume that you know x2. Solve for x 2. Relevant equations 3. The attempt at a solution a) This is easy, the column space of A is just the range of A. b) Do we just use the definitions of R(A) and N(A)? c) I have no idea on this one. Any help please.