Representing a system of equations with $3$ matrices with respective coefficients of $1$, $s$, and $t$

Question

I have a math problem in which I have a system of equations with $4$ variables. I solved it out and it is a dependent. The program I am using is asking for an input in a certain format that I am not familiar with, using a $4\times1$ matrix for the variables and then $3$ more $4\times1$ matrices multiplied by $1$, $s$, and $t$ respectively.

Answer 1

Guide:

If you solve for the system of linear equations using Gaussian elimination and reduce it to an RREF, you should obtain something like

$$\left[\begin{array}{cccc|c} 1 & 0 & A_{13} & A_{14} & b_1 \\ 0 & 1 & A_{23} & A_{24} & b_2\\ 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0\end{array}\right]$$

Let $x_3=s$ and $x_4=t$.

You should be able to conclude that $x_1+A_{13}s+A_{14}t=b_1$. You should be able to solve for $x_1$ in terms of $s$ and $t$.

Do similar stuff for $x_2$.