\text { Let } T: P_{2}(\mathbb{R}) \rightarrow M_{2 \times 2}(\mathbb{R}) T(p)=\left(\begin{array}{cc} 0 & p\left(a_{5}\right) \\ p^{\prime}\left(a_{4}\right) & 0 \end{array}\right) (1) Prove that T is a linear transformation. 2) Determine the

matrix 'of T with respect to the standard bases of 6,y of P2(R) and Max2(R). \text { (3) Determine }[T(q)]_{\gamma} \text { where } q=a_{1}+a_{5} x+a_{3} x^{2} \text { Find }[T \circ L]_{\beta}^{\gamma} \text {. }