1. The problem statement, all variables and given/known data if Ax = b has a solution and A^Ty = 0 , is y^T(x) = 0 or y^T(y) =0 2. Relevant equations 3. The attempt at a solution I simply do not think i understand the properties to answer this question. From my understandinging, the transpose of A times y is = 0. This means that A transpose and y(all the members of these two subspaces) are perpendicular. Does this indicate that y is essentially the nullspace of A transpose? A transpose is the rowspace? Where do I progress on frmo this? I'd like to add... why is the transpose of these matrices even relevant? I don't understand. Are there properties of the transpose that I'm missing? What are these variables y and x representing? There's just so much here that's confusing me(I'm guessing I don't understand fundamentally) I know that the row space is orthogonal to the nullspace(and colspace with the left nullspace) how do i use this knowledge to solve this problem?