(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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?

2. Relevant equations

3. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: A basis

**Physics Forums | Science Articles, Homework Help, Discussion**