In an exercise I'm asked the following:
Let $F$ be a subspace of $\Bbb R ^4$ represented, in relation to certain base, by the system of equations: $$\begin{cases} x_1 + x_2 = 0 \\ x_1 - x_3 = 0 \end{cases}$$ Determine a system of equations that represent $F'$ such that $F' \leq \Bbb R^4$ and $\Bbb R^4 = F'\oplus F$
In this exercise, the teacher introduced the variables $x_1,x_2$ and $x_3$ without saying what they were. I suppose that those are the coordinates $(x_1,x_2,x_3)$ in relation to the basis they refer, and then $F$ would be the set of the points whose coordinates satisfy the equation. But I'm not sure.
I am asking, to someone who is familiar with the concepts used here, if you can figure out by the context what those variables are. If possible I would also want some help/tips for solving this exercise. Thank you.