# vector spaces and linear spans

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.

https://brainmass.com/math/vector-calculus/vector-spaces-linear-spans-443497

#### Solution Preview

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 ...

#### Solution Summary

This solution carefully addresses vector spaces and linear spans.

$2.19