Find values a and b that satisfy a∙〈5,-4,0〉+b∙〈2,2,-3〉=〈11,-16,-6〉.

Therefore a = 5 and b = 2

Step-by-step explanation:

Given,

a (5,-4,0) + b (2,2,-3) = (11,-16,-6)

⇔ (5a,-4a, 0) + (2b, 2b,-3b) = (11,-16,-6)

⇔ (5a+2b,-4a+2b,-3b) = (11,-16,-6)

Therefore

5a+2b = 11 ... (1) - 4a+2b=-16 ... (2) - 3b=-6 ... (3)

From equation (3) we get

-3b = - 6

⇔b = 2

Putting the value of b in equation (2)

-4a + 2.2 = 16

⇔-4a = - 16-4

⇔ a = 5

Therefore a = 5 and b = 2