$(3)$ Let $T_1$:$M_2(R)P_2(R)$ be defined by

$T_1(\left[\begin{array}{cc}a& b\\ c& d\end{array}\right])=(a+b)+(b+c)X+(c+d)2$

and let $T_2$:$P_2(R)P_1(R)$ be defined by

$T_2(P(x))=P^{\text{'}}(x).$

Determine ker$(T_2{T}_1),Rng(T_2{T}_1)$ and their dimansions.