# Thread: change of basis help?

1. ## change of basis help?

Problem is assuming the mapping T: P2---->P2 defined by T(a0+a1t+a2t2)=3a0+(5a0-2a1)t+(4a1+a2)t^2 is linear. Find the matrix representation of T relative to Basis B={1,t,t^2}.
The part that im confused on is when I go plug in the basis values T(1),T(t),and T(t^2)? I don't know how to do it?

From my understanding T(a0+a1t+a2t2) can be written as a0T(1)+a1T(t)+a2T(t^2)
So to find T(1) its just a0T(1)+0T(t)+0T(t^2)=3a0+5a0t? Am i right?