I need to prove this:
If The columns of A span Rn, then The equation Ax = b has at least one solution for each b in Rn
Step by step please....i really want to understand this...thanksthanks
If the columns of A span ℝn, it means that for every b ∈ ℝn there exist numbers x1, ..., xn such that x1A1 + ... + xnAn = b, where Ai is the ith column of A. But this exactly means that Ax = b has the solution x = (x1, ..., xn).