Let 𝐚=⟨2,4,2⟩ a = ⟨ 2 , 4 , 2 ⟩ and 𝐛=⟨−4,0,3⟩ b = ⟨ − 4 , 0 , 3 ⟩ . Show that there are scalars 𝑠 s and 𝑡 t so that 𝑠𝐚+𝑡𝐛=⟨−18,−4,10⟩

Question

 Let  and . Show that there are scalars  and so that 

s=

t=

Answer 1

2s -4t = -18

4s +0t=-4

2s+3t= 10

s = -1

From 1st equation

-2-4t=-18

t = 4

Checking:

2(-1)+3(4) = -2+12 = 10 √