Finding a system of linear equations whose solution space is $\langle a_1,a_2,a_3\rangle$

Question

I am trying to do a problem for linear algebra and I have run into a problem I have no idea how to solve. The problem is:

Find a system of linear equations whose solution space is the subspace $\langle a_1,a_2,a_3\rangle$ of $\mathbb R^5$, where $$a_1=(1,-1,0,1,-1);\ a_2=(1,-1,-1,0,1);\ a_3=(1,0,1,-1,1).$$

I am not even sure what topic this is. Could someone provide me with a method to follow or even the name of the topic so I can search for some online resources to learn a method.