Abstract and Linear algebra

Question

If the linear transformation T: R ^ 3 to R ^ 2 which maps the basis vectors ((1,0,0), (0,1,0), (0,0,1)) of R ^ 3 to the vectors [ (1, 1), (2, 3) , (3, 2) ] respectively. Then T(1, 1, 0) is equal to

Answer 1

Since T is linear we have that T(1,1,0)=T(1,0,0)+T(0,1,0)=(1,1)+(2,3)=(3,4).