Hi. I need help understanding this question:
The question tells us to state why the following is not a linear transformation:
Their answer is simple enough:
There's a property: T(-v) = -T(v)
however, T(-(1,1) ǂ -T(1,1) (by the way, is there a way to post the not equal sign in Latex. I just copy pasted from character map)
therefore, it is not a linear transformation.
But I am having trouble solving the question using the main two properties:
T(a+b) = T(a) + T(b)
T( ) =
I started like this:
T(x,y) = (x^2, xy)
T(a+b) = T( )=
=( , )=
= ( ), ( )
and from here I am having trouble proving or disproving if it equals T(a) + T(b).
Can someone help?