# Homework Help: Find a basis for a set S of R4

1. Sep 26, 2012

### ElijahRockers

1. The problem statement, all variables and given/known data

Find a basis for the subspace S of vectors (A+B, A-B+2C, B, C) in R4

What is the dimension of S?

3. The attempt at a solution

Do I just plug in varying values for A B and C to create four vectors, and see if they are linearly independent? If they are then I've found a basis?

2. Sep 26, 2012

### voko

Making any two of A, B & C zero results in a vector in S. How many such vectors are there?

3. Sep 26, 2012

### LCKurtz

Or, similar to voko's observation write it like this:$$A(1,1,0,0)+B(1,-1,1,0)+C(0,2,0,1)$$and see if that helps.