Define a linear transformation $T: P_2 \rightarrow R^2$ by $T(p) = \left[ \begin{array}{cc}P(0)\\P(0) \end{array} \right]$. Find polynomials $p_1$ and $p_2$ in $P_2$ that span the kernel of $T$, and describe the range of $T$.
2. $kerT=\{p \in P_2:T(p)=0\}=\{p \in P_2(0)=0\}" alt="kerT=\{p \in P_2:T(p)=0\}=\{p \in P_2(0)=0\}" />
the range of T is the subspace of $R^2$ generated by (1,1).