Question

Use counter example to show that the funtion T: R2->R3 given by T(x1, x2) = (x1^2,x2,x1+x2) is not a linear transformation from R2 to R3.

Answer 1

Let \(u=(1,3)\)
For \(T(u)\) to be a linear transformation, we must have \(T(2u) = 2T(u)\)

simply show that above is not satisfied

Answer 2

\(T(2u)=T(2*1, 2*3)=T(2,6)=(2^2,6,2+6)=(4,6,8)\)

\(2T(u) = 2T(1,3)=2(1^2,3,1+3)=2(1,3,4)=(2,6,8)\)

\(T(2u)\ne 2T(u)\)
so \(T\) is not a linear transformation

Answer 3

Okay I understand now! Thanks!

Answer 4

yw