Given a transform $\bR^m \to \bR^n$,
get an $n\times m$ matrix;
row operations act on target, and leave kernel invariant;
column operations act on domain, and leave image invariant.

Given a matrix:
- column-reduced form gives nice basis for image
- row-reduced form can read off basis for kernel easily
  say it's:
  1 2 0 3
      1 5
  free variables are x2, x4
  pivots are determined
  so kernel is
  (-2x2-3x4,x2,-5x4,x4)
