I have this problem to solve:

Find two independent vectors on the plane x + 2y - 3z -t = 0 in R4. Then find 3 independent vectors. Why not four? This plane is the nullspace of what matrix.

I am having difficulty seeing the problem. My first thought is to set up a 4 x 4 matrix with 1 2 -3 -1 as the first row and try to find other entries to row reduce it to a matrix with 2 pivots. Can anyone help and give me suggestions if I am close or not? Also, if anyone has a good explanation for why it is not possible to get 4 independent vectors. Thanks!!