1. The problem statement, all variables and given/known data Find a basis for the subspace S of R^4 consisting of all vectors of the form (a+b, a-b+2c, b, c)^T, where a,b,c are real numbers. What is the dimension of S? 2. Relevant equations vectors v1,...,vn from a basis for a vector space iff i) v1,...,vn are linearly independent ii) v1,...,vn span V 3. The attempt at a solution I'm actually not sure how I'd start this problem as most of the basis problems I've been doing have been comparing 2-3 vectors against each other not just one. Would I have to find a vector of scalars in R^4 and find S is both linearly independent and spans R^4 against it? any help is greatly appreciated.