show that each function is a linear tranformation T(x,y)=(2x,x+y,x-2y) (T:R²=>r³)

Question

(2) T:R³=>M^(2,2) given by T(x,y,z)=[y 2]
[2 0]

Answer 1

i tried to make a matrice bracket but i couldn't

Answer 2

(1) since each of the images is a linear combination of x,y T is a linear transformation.
(2) is the same
Remember, all you have to show is that
T(a+b) = T(a)+T(b)
T(ka) = kT(a)

Answer 3

i think i get it now perfectly