# linear transformation

For each of the following functions decide whether or not the function is a linear transformation. Prove your answer in each case:

(a) F: V3(R) --> V2(R) defined by F(a1, a2, a3) = (2a1 - a2, 3a3)

(b) G: V3(R) --> V2(R) defined by G(a1, a2, a3) = (a1 - a2 + a3, a1 + a2a3)

https://brainmass.com/math/linear-algebra/solving-linear-transformation-problems-299002

#### Solution Preview

Hi,

Please find the solutions/explanations attached herewith.

I hope it will help.

Thanks

Solution part(a):

Let u = (u1, u2, u3) and v = (v1, v2, v3)

(u + v) = (u1+v1, u2+v2, u3+v3)

F(u + v)

= F(u1+v1, u2+v2, u3+v3)

= (2(u1+v1)-(u2+v2), 3(u3+v3))

F(u) = (2u1 -u2, ...

#### Solution Summary

A linear transformation is embodied.

$2.19