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Let $T: R^{2} ightarrow R^{3}$ be defined by $T=left(left[begin{array} {1}x_{1} x_{2} end{array} ight] ight)=left[begin{array}{c}x_{1}+8 x_{2} -x_{1} end{array} ight]$ Find the matrix $[T]_{B^{prime}, B}$

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Let $T: R^{2} ightarrow R^{3}$ be defined by $T=\left(\left[\begin{array} {1}x_{1} \\x_{2} \end{array} ight] ight)=\left[\begin{array}{c}x_{1}+8 x_{2} \ -x_{1} \\ \end{array} ight]$ Find the matrix $[T]_{B^{\prime}, B}$ relative to the bases $B=\left\ {\boldsymbol{u}_{1}, \boldsymbol{u}_{2} ight\}$ and $B^{\prime}=\left\{v_{1}, v_{2}, V_{3} ight\}$, where $$ u_{1}=\left[\begin{array}{1} 11 3 \end{array} ight], \quad u_{2}=\left[\begin{array}{c} -21 4 \end{array} ight], \quad v_{1}=\left[\begin{array}{1} 1 11 1 \end{array} ight], \quad v_{2}=\left[\begin{array}{1} 21 21 0 \end{array} ight], quad v_{3}=\left[\begin{array}{1} 31 OW 0 \end{array} ight] $$ NOTE: Enter the exact values. $$ [T]_{B^{\prime}, B}=\left(\begin{array}{11} ? & ? ? & ? ? & ? \end{array} ight) $$ CS.JG. 124

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