2nd Year Linear Algebra help.

[SizableSac]

Well i have this assignment due monday and any help i could get with this would be very appreciated.. The sad thing is that i dont know how to FIND the transformation (T) in the first question and a lot of other questions ask to find the transformation so im kinda screwed there -.-

Heres the assignment http://hotfile.com/dl/104123079/479cdce/Assign.pdf.html

[SizableSac]

If anyone can explain how to find/express the linear transformations that would be great

[Mantikore]

Ok, im in a bit of a hurry and i just woke up, so if anyone spots a mistake, i am sorry, but having a quick look at it:

1) One of the conditions of linear maps is that
T(x1 + x2) = T(x1) + T(x2) that is, addition is closed
you have T(x^2) and T(x+1).
so T(x^2 + x + 1) is just T(x^2) + T(x+1)
which is x^3 + 0 = x^3

2) two of the easiest tests you can do to test for non linearity is
T(0)=0 and T(-v) = -T(v). if it fails one test, its not linear. of course, it is very possible for it to not be linear and pass.
obviously, it wouldnt fail the first one, but it does fail the second
T(-x,-y) = (-x-y, xy)
-T(x,y) = -(x+y, xy)
=(-x-y, -xy)

so its not linear.

ill be back later. hopefully in time

[SizableSac]

Thanks for your help so far Umm so how would i find T for question 1? I understand what youve said so far so thanks

[threat]

I don't know but maybe this will help...

http://www.khanacademy.org/

[SizableSac]

Haha tried that site already