Answer to Question #35165 in Linear Algebra for Matthew Lind

Question

We have W = {w^1,...,w^n} as a spanning set for a subspace S in R^j, and V = {v^1,...,v^m} a linearly independent subset of S. Let A be the matrix whose columns are the v^m, B the matrix whose columns are the w^n. Please show that there is an N by M matrix C such that A = BC.