If you have two hyperplanes in R^5 given as... H1 = (1, -2, -5, 0, 1)^T.x = 0 H2 = (0, 1, 0, 1, -1)^T.x = 0 (where ^T is transpose) Then S, which is a subspace of the 5th dimension, is simply the intersection of H1 and H2, ie. H1 n H2. I got this intuitively since the planes pass through the origin. 1) How would you prove this? 2) For any x the system holds as a solution to Ax = 0. But is it possible to row-reduce the system Ax = 0 to row-echelon form and use this to find a basis for S? Thankyou for any assistance or guidance on this matter.