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14. Write the matrix representations of the linear operators with respect to the ordered basis $\mathcal{B}$. (a) $T: M_2(\mathbb{R}) \rightarrow M_2(\mathbb{R})$ such that $$T\left(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\right) = \begin{bmatrix} a+d & c \\ c+d & a \end{bmatrix}$$ and $\mathcal{B}$ is the standard basis of $M_2(\mathbb{R})$. (b) $T: \mathbb{R}^2 \rightarrow \mathbb{R}^2$, where $T(x, y) = (x, y)$, and $\mathcal{B} = \{(1, 1), (1, -1)\}$. (c) $\mathcal{D}: P_n(\mathbb{R}) \rightarrow P_n(\mathbb{R})$ such that $\mathcal{D}(a_0 + a_1x + \dots + a_nx^n) = a_1 + 2a_2x + \dots + na_nx^{n-1}$, and $\mathcal{B} = \{1, x, \dots, x^n\}$.

          14. Write the matrix representations of the linear operators with respect to the ordered basis $\mathcal{B}$.
(a) $T: M_2(\mathbb{R}) \rightarrow M_2(\mathbb{R})$ such that
$$T\left(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\right) = \begin{bmatrix} a+d & c \\ c+d & a \end{bmatrix}$$
and $\mathcal{B}$ is the standard basis of $M_2(\mathbb{R})$.
(b) $T: \mathbb{R}^2 \rightarrow \mathbb{R}^2$, where $T(x, y) = (x, y)$, and $\mathcal{B} = \{(1, 1), (1, -1)\}$.
(c) $\mathcal{D}: P_n(\mathbb{R}) \rightarrow P_n(\mathbb{R})$ such that $\mathcal{D}(a_0 + a_1x + \dots + a_nx^n) = a_1 + 2a_2x + \dots + na_nx^{n-1}$, and $\mathcal{B} = \{1, x, \dots, x^n\}$.

14 write the matrix representations of the linear operators with respect to the ordered basis mathcalb a t m2mathbbr rightarrow m2mathbbr such that tleftbeginbmatrix a b c d endbmatrixrigh 64773

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