Let A be an m x n matrix. Prove that
Ax = b has at least one solution
for any b if and only if A has linearly
independent rows.
Let V be a vector space with dimension 3, and let
V = span(u, v,
w). Prove that u,
v, w are linearly independent (in
other words, you are being asked to show that u,
v, w form a basis for
V)