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\text { Define the map } \mathrm{T}: \mathrm{P}_{2}(\mathbb{R}) \rightarrow \mathrm{M}_{2 \times 2}(\mathbb{R}) \text { by } \mathrm{T}(f)(x)=\left(\begin{array}{cc}

f(1)-f(2) & 0 \\

0 & f(0)

\end{array}\right) \text { For example } f(x)=x^{2} \text { is in } \mathrm{P}_{2}(\mathbb{R}) \text {, } \mathrm{T}(f)(x)=\left(\begin{array}{ll}

4 & 0 \\

0 & 0

\end{array}\right) \in \mathrm{M}_{2 \times 2}(\mathbb{R}) Prove that T is a linear map.

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