Suppose that $x_1 = -1$, $x_2 = 2$, $x_3 = 4$, $x_4 = -3$ is a solution of a non-homogeneous linear system $A\mathbf{x} = \mathbf{b}$ and that the solution set of the homogeneous system $A\mathbf{x} =\mathbf{0}$ is given by the formulas: $\begin{align*} x_1 &= -3r + 4s,\\ x_2 &= r - s,\\ x_3 &= r,\\ x_4 &= s. \end{align*}$ Find the vector form of the general solutions of Ax = 0 and Ax = b
I ended up with something like:
( -3 4) ( 1 -1) ( 1 0) ( 0 1)
where I separated the $r$ and $s$ values, I haven't tried to actually solve though because I'm kinda confused about what I'm suppose to do with this.