please help me with this question :For what values (s) of h is y in the plane generated by v1 and v2 ?

Question

Let 

  =  ,    , and = 

For what values (s) of h is  in the plane generated by   and   ?

Answer 1

y is a linear combination of the vectors v₁ and v₂

The vectors multiplied by a scalar produces y

So av₁ + bv₂ = y

We get a system of three equations

a(1) + b(-3) = h

a(0) + b(1) = -5

a(-2) + b(8) = -3

We see b = -5 so now we can solve for a

-2a + (-5)(8) = -3

-2a + -40 = -3

2a = -37

a = -37/2

Solving for h

(-37/2)(1) + (-5)(-3) = h

-37/2 + 15 = h

h = -3.5