Calculus help!! i can't get the right answer.....?

Question

in example 3, we chose vector c and let vector c = sa+tb. (a + b are vectors. Then we found that c= 2a + 3b. what result would we have obtained if we had chosen:

a) b instead of c??

(((( the coordinates from example 3 are a=[1,2,3], b=[2,.1,3] and c=[8,1,15] )))))

the answer is b= -2/3a + 1/3c.


can someone show the work i keep getting it wrong even though i follow the exmaple exactly!!

Answer 1

If you have three vectors a, b, and c and you know:

c = 2a + 3b

It's just basic algebra to solve for b. It doesn't matter what the actual values of the three vectors are.

c = 2a + 3b
-2a + c = 3b
-(2/3)a + (1/3)c = b

b = -(2/3)a + (1/3)c