Let A be a mxn matrix with entries in F and columns A1, A2, ... , An. Let A' be a reduced row echelon form, with pivots in columns p1, p2, ... , pk.
Prove that B= (AP1, AP2, ... , APk) is a basis for Col(A)
Just doing some review and came across this, I don't remember doing much discussion on basis in class and would appreciate help!