Question: Let $T: R^{2} ightarrow R^{3}$ be defined by $T=left(left[begin{array} {1}x_{1}x_{2} end{array} ight] ight)=left[begin{array}{c}x_{1}+2 x_{2} -x_{1} 1 Oend{array} ight ]$ Find the matrix $[T1_{B^{prime), B}

Let $T: R^{2} ightarrow R^{3}$ be defined by $T=\left(\left[\begin{array} {1}x_{1}x_{2} \end{array} ight] ight)=\left[\begin{array}{c}x_{1}+2 x_{2} \ -x_{1} 1 O\end{array} ight ]$ Find the matrix $[T1_{B^{\prime), B} $ relative to the bases $B=\left\{u_{1}, u_{2} ight\}$ and $B^{\prime} =\left\{v_{1}, v_{2}, V_{3} ight\}$, where $$ u_{1}=\left[\begin{array}{1} 1 3 \end{array} ight], \quad u_{2}=\left|\begin{array}{c} -2 11 4 \end{array} ight], \quad v_{1}=\left[\begin{array}{1} 1 11 1 \end{array} ight], \quad v_{2}=\left[\begin{array}{1} 2 11 2 0 \end{array} ight], \quad v_{3}=\left[\begin{array}{1} 3 W OW 0 \end{array} ight] $$ NOTE: Enter the exact values. $$ [T]-{B^{\prime), B)=\left(\begin{array}{11} ? & ? ? &? ? & ? \end{array} ight) $$ CS.JG. 115
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