Thread: Linear Transformation in polynomial vector space

Define T: P1 --> P1 by

T(ax + b) = (2b - a)x + (b + a)

Show that T is both one-to-one and onto, and find the inverse transformation to T.

This problem showed up in my homework, and I'm not sure how to finish it. I was able to prove that T is both on-to-one and onto, but don't know how to find T^(-1). I hope someone can help. Thanks in advance!

Originally Posted by dan213

Define T: P1 --> P1 by

T(ax + b) = (2b - a)x + (b + a)

Show that T is both one-to-one and onto, and find the inverse transformation to T.

This problem showed up in my homework, and I'm not sure how to finish it. I was able to prove that T is both on-to-one and onto, but don't know how to find T^(-1). I hope someone can help. Thanks in advance!

Let and be the basis vectors for


Then
and


So the matrix representation of the linear transformation is



Can you finish finding the inverse from here?

Yes I can - thank you. I appreciate your help.