Find a and b

Question

Find a and b such that 

 

[18,24,13] = a [1,-2,1] + b [4,4,3].

 

a=?

b=?

Answer 1

When multiplying and adding vectors, you treat each component separately. The vector equation you've written can be re-written as 3 separate equations, which you should be able to solve using basic algebra.

 

18 = 1a + 4b

24 = -2a + 4b

13 = 1a + 3b

 

(I get a = -2, b = 5)