Your proof does not make sense because T(x) is not defined.
However if
So
Whilst
For the second part.
but
I have to either show that a transformation is either linear or not due to the additivity or the homogeneity.
The first question is:
T(x,y)=(x+1,y)
I answered:
T(x)+T(y)= mx+my
m(x+1)+my= mx+m +my
mx+my =/= mx+m+my
therefore
T(x,y)=(x+1,y) is not linear under additivity.
How would I prove or disprove that the transformation is linear under homogeneity?
So I'm guessing I sorta combined the two into an epic fail? I think I understand... Probably not.
A second question is:
T(x,y)=(y,y)
For this, I would have:
let
then
and
T(\vec a) + T(\vec b)=?
I'm not sure what needs to be done here...
For the second part, I'm not sure how to do what you did above using two different vectors, because I would be comparing x to y at some point, correct?
Sorry for my idiocy, by the way.