Can someone explain how to get this answer please.

Let and be the subspaces of defined by

and

Find basis for and and

Now i can find basis for and fairly easily tho they were different from the ones given in the solutions. Problem is i have no idea how to calculate . This is the solution given.

(-2, 1, 0, 0), (1, 0, 1, 0) and (1, 0, 0, 1) form a basis for

(1, 1, 0, 0), (-1, 0, 1, 0) and (-1, 0, 0, 1) form a basis for

(-1, 2, 3, 0), (-1, 2, 0, 3) form a basis for

can someone explain this? It just says clearly this is the basis in the solution... Maybe clear for someone whos been studying it for 30+ years... I can sorta see where the -1 and 2 come from but not the 3's. Any help please?

Thanks