A linear algebra questions, please help!

Question

Given vectors u, a, v, and b as defined below, let T : R2 → R2 be a linear transformation that maps the vector u to the vector a and the vector v to the vector b. Use the linearity of T to find the image of 3u + v.

 

u= -3  a= -13  v= 4  b= 6

     4          6         6      -8 

Answer 1

u = <-3,4>    a = <-13,6>    v = <4,6>     b = <6,-8>

 

T(3u + v) = T(3u) + T(v)

 

                = 3T(u) + T(v) = 3<-13, 6> + <6, -8>

 

                                        = <-39, 18> + <6, -8>

 

                                        = <-33, 10>