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Problem 3. Let $P_{n}$ denote the set of polynomials of degree less than or equal to $n$, and define the linear transformation $L:P_{2}?P_{1}$ by $L(p(x))=dxdp?$ Let $S={x_{2},x+1,2}$ be a basis of $P_{2}$ and $T={2t,1}$ be a basis of $P_{1}$. Find the matrix of $L$ with respect to $S$ and $T$.

The linear transformation L is defined as L(p(x))=ddxp(x). In order to determine the matrix for L we first find the image of the elements of S and wri