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## Homework Statement

Find a basis for the subspace

S = {(a+2b,b-a+b,a+3b) | a,b [tex]\in[/tex] R } [tex]\subseteq[/tex] R^4

What is the dimension of S?

## Homework Equations

## The Attempt at a Solution

a(1,0,-1,1) + b(2,1,1,3) , a,b [tex]\in[/tex] R

span { (1,0,-1,1) , (2,1,1,3) }

So I put (1,0,-1,1) as V1 and (2,1,1,3) as V2 and then formed a matrix with V1 and V2 in columns. Then i reduced it to row echelon form. The column corresponding to the leading entry form a basis which is essentially just (1,0,-1,1) and (2,1,1,3) . Thus the dimension is just 2. Am I doing the right thing because I dont have an answer to refer to.