CH 4

Ax=b, kernel is x, b is range
Kernel is null space is set of sols to Ax=0

Rm->Rn, ker is subspace of Rm and range is subspace of Rn

T is 1to1 iff ker is only zero vector, nullity is 0 if 1to1

If every row has pivot, cols of nxm span Rn and is onto, rank is n

Range is span of columns of A

Pivot cols in echelon form point to indep vecs in matrix

Unif theorem: every col is pivot col, unique solution to Ax=b, range is span of col vectors (e.g. Rn)