Finding a Subset of S that is a Basis for <S>

[jeffreylze]

Homework Statement

After sorting out basis, now I encountered a new term, Subset. And I get all confused again, clearly I'm not good at these, but I am learning.

Let S = {(1,-1,2,1) , (0,1,1,-2) , (1,-3,0,5)}
Find a subset of S that is a basis for <S>

Homework Equations

The Attempt at a Solution

I formed a matrix and row reduced it to row echelon form. Then the corresponding columns on the leading entry gives the basis which is {(1,-1,2,1) ,(0,1,1,-2)} . But now, to answer the question, how to find a subset ? and also, what does <S> mean ? Is that a symbol for a basis?

 

[Dick]

S is the original set of three vectors. <S> means the subspace spanned by the vectors in S. When you did your matrix exercise you found a basis for the subspace consisting of {(1,-1,2,1) ,(0,1,1,-2)}. That IS a subset of S. You are all done. The question was just to find a basis for the subspaces consisting of vectors from S. That's all.