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## Homework Statement

Let H be the set of all vectors of the form [itex](a-3b, b-a, a, b)[/itex] where [itex]a[/itex] and [itex]b[/itex] are arbitrary real scalars. Show that H is a subspace of [itex]ℝ^4[/itex] and find a basis for it.

Right, I've shown it's a proper subspace, just need help with finding a basis. Is [itex]{a-3b, b}[/itex] a suitable basis for this?

I achieved this but putting the vectors into matrix form

1 -3

-1 1

1 0

0 1

Reducing them to end up with

1 -3

0 0

0 0

0 1

Is this a proper way to solve this question? Thanks in advanced.