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Let $T:P_{2}→P_{3}$ be $T(p)=xp(x)$. Write the matrix of $T$ with respect to the bases $B_{1}={1,x,x_{2}}$ for $P_{2}$ and ${1,(x+1),(x+1)_{2},(x+1)_{3}}$ for $P_{3}$. With respect to $B_{1}$ defined in $Q9$, let $B_{3}={2,x−$ $1,1−x_{2}}$. Calculate $[Id]_{B_{1}}$ and the inverse of this last matrix without doing any matrix inversion.

To find the matrix representation of the linear tansformation with respect to the given bases, we...