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

Find the dimnesion and a basis of vector space V

2. Relevant equations

V is the set of all vectors (a,b,c) in R^3 with a+2b-4c=0

3. The attempt at a solution

(4c-2b,b,c) = b(-2,1,0) + c(4,0,1)

so {(-2,1,0),(4,0,1)} is the basis of the SUBSPACE of V right?

how do I get the 3rd linearly independent vector so that it forms the basis of V?

Is it (1,0,0)? (0,1,0) seems possible... but the basis of a vector space isn't unique right?

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# Homework Help: Vector space

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