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## Homework Statement

Let S={(1,2,3,4),(-1,2,0,1),(1,0,1,1),(-2,2,1,0)}. Determine whether or not S is linearly independent. If not, write one of the vectors in S as a linear combination of the others. Find a subset of S which is a basis of the subspace of R

^{4}spanned by S.

## The Attempt at a Solution

I put the 4 vectors into matrix form, and reduced it to get:

[1 2 3 4]

[0 2 2 3]

[0 0 -1 -1]

[0 0 0 -2]

So they are linearly independant. Since S has a rank of 4, it spans R

^{4}. So any basis of the subspace of R

^{4}should be spanned by S.

My subset of S which is a basis of the subspace of R

^{4}and spanned by S is:

{(1,0,0,0),(0,1,0,0),{0,0,1,0),{0,0,0,1)}

Is this correct? I'm not quite sure what they mean by a subset of S.