Recent content by fackert

  1. F

    Undergrad Solution x spanning columns of A

    This is a really odd question to me. Usually we talk about b (in Ax=b) spanning the columns of A but here its talking about x spanning A. If x=<-3,4,8> (this is a vertical 3x1 matrix) is a solution to Ax=0, then is x in the set spanned by the columns of A? I'm pretty sure it is no, but i...
  2. F

    Graduate Determinant of row interchange proof

    Need a lot of help here guys. I need to prove that for an nxn matrix A, if i interchange two rows to obtain B, then det=-detA I have proved my basis (below), but I'm stuck on the hard part, the induction (which I'm required to do). I understand the steps of induction, but i don't know how...
  3. F

    Undergrad Why is it not possible for the columns of a matrix to span R^2 even if

    Why is it not possible for the columns of a matrix to span R^2 even if those columns do not span R^3?