Write the vector w 321 as a linear combination of vectors i

Write the vector w = (3,2,1) as a linear combination of vectors in the set S = {(1, 1, 1), (1, 1, 0), (1, 0, 0)}.

Solution

Let (3 2 1)=a(1 1 1)+b(1 1 0)+c(1 0 0)

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

Therefore 3=a+b+c

2=a+b

1=a

Therefore a=1

b=1

C=1

Therefore (3 2 1)= 1(1 1 1)+1(1 1 0) +1(1 0 0)