A = [?1 ?2; ?1 2]. Let T be a linear transformation from ?² to ?² with associated matrix B = [3 ?2; ?1 3]. Determine the matrix C of the composition T ? S. C =
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Let S be a linear transformation from R2 to R2 with associated matrix A = [1 2; 3 2]. Let T be a linear transformation from R2 to R2 with associated matrix B = [1 0; -2 0]. Determine the matrix C of the composition T o S.
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Determine the matrix representation $[T]_{B}^{C}$ for the given linear transformation $T$ and ordered bases $\bar{B}$ and $C$. $T: M_{2}(\mathbb{R}) \rightarrow \mathbb{R}^{2}$ given by $$T(A)=(\operatorname{tr}(A), \operatorname{tr}(A))$$ (a) $B=\left\{E_{11}, E_{12}, E_{21}, E_{22}\right\} ; C=\{(1,0),(0,1)\}$ (b) $B=\left\{\left[\begin{array}{cc}-1 & -2 \\ -2 & -3\end{array}\right],\left[\begin{array}{ll}1 & 1 \\ 2 & 2\end{array}\right],\left[\begin{array}{cc}0 & -3 \\ 2 & -2\end{array}\right],\left[\begin{array}{ll}0 & 4 \\ 1 & 0\end{array}\right]\right\}$ $C=\{(1,0),(0,1)\}$
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