Find a basis for a set S of R4

[ElijahRockers]

Homework Statement

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

What is the dimension of S?

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?

 

[voko]

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

 

[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.