Adding for example you'll get a rank 4 matrix, that is the columns are linearly inedependent. Now use that linearly independent vectors in a vector space of dimension form a basis of .
given two vectors:
i need to come up with two more vectors (eg U_1 and U_2) which when in a set with the first two create a basis for R^4. i tried using like a1,b1,c1,d1 for each u_1 and U_2 and getting it into REF but i had no joy. apparently according to my friend you should be able just to guess the vectors which satisfy this.