Let V be $ C[x]/(x^3+5x^2+6x+2) $ and let $ T:V→V $ be defined by $T(p(x))=(x+1)p(x) $. I need to find the bases for the kernel (null space) and image (range) of T.
I have to write T in matrix form right? After that we can easily find the bases. How can we write it in matrix form? Also one more puzzling thing is that do we take $p(x)=x^3+5x^2+6x+2$.