Here's what I would have submitted: Question 1: Clearly 0=A0 is in col A. If u=Ax and v=Ay are in col A, then u+v=Ax+Ay=A(x+y) which is in col A. If u=Ax in col A and c a scalar, then cu=cAx=A(cx) which is in col A. Thus col A is a subspace. Question 2: [-2 ] [-2] [ 1 ] [-2] [ 1 ],[ 0] [ 0 ] [ 1] [ 0 ] [ 0] Question 3: [ 1] [5] [4] [ 4] [1] [3] [-1], [5], [3] [-2] [4] [1] [-2] [2] [3]