# Find bases for the following subspace of F^5

## Homework Statement

Find bases for the following subspaces of F^5:

W1 = {(a1, a2, a3, a4, a5) E F^5 : a1 - a3 - a4 = 0}

and

W2 = {(a1, a2, a3, a4, a5) E F^5: a2 = a3 = a4 and a1 + a5 = 0}

2. The attempt at a solution

Well, I understand a basis is the maximum amount of vectors in a set that are linearly independent, or the smallest amount of L.I vectors that span a space. What is throwing me off is the constraints a1 - a3 - a4 = 0 and a2 = a3 = a4 and a1 + a5 = 0