For what value of h is y in the plane spanned by v1 and v2?

Question

Let v1= [-2 3 2] , v2= [4 -4 -5] , and y= [-18 19 h]

Answer 1

A vector is in the span of v₁ and v₂ if it is of the form av₁+bv_2. Therefore, we will have a system of equations to have y in the span of v₁ and v₂,

-18=-2a+4b

19=3a-4b

h=2a-5b.

From the first two equations, we will have a=1 and b=-4. Then h=22.