At the last proof (A'A is invertible), why is he allowed to multiply both sides by a row vector? Shouldn't that change the solution set?For example, suppose [x1 x2 x3 x4]' = 0. Then x = 0 vector. But if I multiply both sides by [1 -1 0 0], then [1 1 0 0]' becomes a solution. Should I assume that this operation can only add solutions, so the proof is still valid (since after the operation, only 0 is in the nullspace)?####[['row vector', 'Mathematical_Related_Concept', 'NEG'], ['operation', 'Mathematical_Related_Concept', 'NEU']]