# Linear algebra: System of equations problem

I have been doing one exercise and got a problem. The exercise is as follows:

Now, in the beginning of solutions it says that one should first find the solution space V for the system of equations: photo2 And that the solution space V is consisted of all vectors v of form:

I do not understand how did they get this form for the vector v. If I do Gauss Jordan on the equation system, I get a different solution. This is one point of this task that I do not understand. The next steps for getting to the final solution are easy. (Please help me get a few more rep so that I can post photos, not links, thanks)

• You should also show your solution for the system and hiw you have derived it. Have you checked whether the vectrors given in the solution satisfy the system? what is the rank you obtain? – gimusi Mar 22 '18 at 2:36
• please learn mathjax. photos are not searchable and we want to help people to search for similar posts. – Siong Thye Goh Mar 22 '18 at 2:39

$$x_1-x_2-x_3-3x_4=0$$
$$x_1-2x_2+x_3+x_5=0$$
Let $x_2=r, x_3=s, x_4=t$, solve for $x_1$ and $x_5$ in terms of $r,s,t$.