(adsbygoogle = window.adsbygoogle || []).push({}); 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.

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# Homework Help: LA: basis for a subspace

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