For the given matrix $A = \begin{bmatrix} 1 & 1 & 3 & 1 \\ 2 & 1 & 5 & 4 \\ 1 & 2 & 4 & -1 \end{bmatrix}$, the RREF was found to be: $$x_1 = -2x_3 - 3x_4$$ $$x_2 = -x_3 + 2x_4$$ $$x_3,x_4 = free$$
How would we determine two vectors $u_1$ and $u_2$ such that any vector in the null space $A$ could be written as a linear combination of those two vectors. Similarly, how would we determine two vectors that would could fulfill the same condition in the range space $A$?