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Find bases for the following subspace of F^5

  • #1

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
 

Answers and Replies

  • #2
radou
Homework Helper
3,115
6
Well, the constraints give you an idea of how a characteristic element of the subspace should look like. For example, in W2 you have an element (a1, a2, a2, a2, -a1) = a1(1, 0, 0, 0, -1) + a2(0, 1, 1, 1, 0). This should give you an idea.
 

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