Calculus Question

Question

Find (if possible) y and ß such that (all letters with arrows on top symbol (vectors)) c = ya + ßb where a = (2,0,-3), b = (0,-3,4) and c = (-6,6,1).

Answer 1

-6 = 2γ + 0β

-3 = γ

6 = 0γ - 3β

-2 = β

γa = -3<2, 0, -3>

γa = <-6. 0. 9>

βb = -2<0, -3, 4>

βb = <0, 6, -8>

Verify:

γa + βb = c