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vector spaces and linear spans

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Find all real numbers k such that the vector v=(1,-2,k) in R^3 (with the usual operations) is
in the linear span of the vectors x=(3,0,-2) and y=(2,-1,-5).
Prove your answer. Be sure to address both necessity and sufficiency. Show all work.

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This solution carefully addresses vector spaces and linear spans.

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Find all real numbers k such that the vector v=(1,-2,k) in R^3 (with the usual operations) is
in the linear span of the vectors x=(3,0,-2) and y=(2,-1,-5).
Prove your answer. Be sure to address both necessity and sufficiency. Show all work.

If the given vector v to be in the linear span of the vectors x and y, we should have some scalars a and b such that v=ax+by
This gives the relation ...

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