Let V=S2x2 (2x2 real symmetric matrices) with basis (1,1;1,0) (0,1;1,0) (1,0;0,1) and let W=P2(R) with basis {x^2,x+1,1-x}.

Let the images of the basis vectors of V be 2x-2, x^2+x+1, and 3x^2+2 respectively. Find T^-1(f).

Can someone explain this? I can do it in standard bases but this gives me trouble. Thanks!