Simple linear operator

May 2010
20
1
I have dosed off in class way too many times and I need help with a few problems:

#1
Suppose T: P_2 -> P_2 is a linear operator and
T(1)=2+3x
T(x)=1+x^2
T(x^2)=5-x+3x^2
Find T(2-x+2x^2)

A simple hint in the right direction would be greatly appreciated.

Advathanksnce!
 
Last edited:
Oct 2009
4,261
1,836
I have dosed off in class way too many times and I need help with a few problems:

#1
Suppose T: P_2 -> P_2 is a linear operator and
T(1)=2+3x
T(x)=1+x^2
T(x^2)=5-x+3x^2
Find T(2-x+2x^2)

A simple hint in the right direction would be greatly appreciated.

Advathanksnce!

By linearity, \(\displaystyle T(2-x+2x^2)=2T(1)-T(x)+2T(x^2)=\) ...and stop dossing off in math classes!(Punch) For that there exist religion, sociology, accounting and other hyperboring classes.

Tonio
 
May 2010
20
1
By linearity, \(\displaystyle T(2-x+2x^2)=2T(1)-T(x)+2T(x^2)=\) ...and stop dossing off in math classes!(Punch) For that there exist religion, sociology, accounting and other hyperboring classes.

Tonio
Thanks for the help! I dose off equally in my other classes as well :eek: