I am working from Erwin Kreyszig's book, where he mentions of a question.
Is the given set of vectors a vector space. If yes, determine the dimension and find a basis $(v_{1},v_{2},\cdots,v_{n} )$ denote components
All vectors in $\mathbb R^{3}$, such that $4v_{2}+v_{3}=k$
I have an intuitive understanding of vector space, as the output of a generator set (aka spanning set formed via basis set), is there a test for proving a particular set is a Vector Space?
Secondly, given this condition on $v_{2}$ and $v_{3}$ how do I go ahead to find the basis? I understand finding dimension from basis is a trivial exercise.
Help much appreciated
P.S: Apologies for formatting, but I am not able to render latex on my post. An additional link to some help would be much appreciated