For what value of h is y in the plane spanned by v 1 and v 2

For what value of h is y? in the plane spanned by v? 1 and v? 2?

Let v_1 = [-2 5 4 ], v_2 = [6 -13 -16], y = [28 -62 h].| For what value of h| is y| in the plane spanned by V_1| and v_2|? h =|

Solution

If y is in the plane spanned by v1 and v2, then y must be a linear combination of v1 and v2. That is, there must exist scalars s and t such that

y = s v1 + t v2

( 28 , -62, h) = s( -2 , 5 , 4) +t(6 , -13 , -16)

-2s +6t = 28

5s -13t = -62

h = 4s -16t

Solve equation 1 and 2: we get s= -2 ; t=4

h = 4s -16t = 4*(-2) -16(4) = -8 -64 = -72

h = -72