Linear Transformations and Isomorphismsby blondie1234 Tags: isomorphisms, linear alegbra, transformations 

#1
Apr1910, 06:17 PM

P: 2

1. Find out which of the transformations are linear. For those that are linear, determine whether they are isomorphisms. T(f(t)) = f'(t) + t^2 from P2 to P2
2. To be linear, T(f(t)+g(t))=T(f(t)) + T(g(t)), kT(f(t))=T(f(kt)) 3. After testing for linearity, I am thinking that the equation does not fulfill the requirements and therefore there are no isomorphisms, but I'm not sure if I did it right. First, I said that: T(f(t)+g(t))=(f'(t)+g'(t))+ t^2 and T(f(t) + T(g(t))= f'(t)+t^2+g'(t)+t^2=f'(t)+2(t^2)+g'(t) which is not equal to the first, therefore it is not linear. Am I going in the right direction with this? 1. The problem statement, all variables and given/known data 2. Relevant equations 3. The attempt at a solution 



#2
Apr1910, 07:10 PM

Sci Advisor
HW Helper
Thanks
P: 25,167

You are doing it right. It's not linear.



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