Question: Given \(T:\left( \left[ \begin{array}{*{35}{l}} {{x}_{1}} \\ {{x}_{2}} \\ {{x}_{3}} \\ \end{array} \right] \right)=\left[ \begin{array}{*{35}{l}} 2{{x}_{1}}+{{x}_{3}} \\ {{x}_{1}}+{{x}_{2}}-{{x}_{3}} \\ \end{array} \right]\)

and

\(U\left( \left[ \begin{array}{*{35}{l}} {{x}_{1}} \\ {{x}_{2}} \\ \end{array} \right] \right)=\left[ \begin{matrix} 3{{x}_{1}}-{{x}_{2}} \\ {{x}_{2}} \\ {{x}_{1}}+{{x}_{2}} \\ \end{matrix} \right]\)

Determine the standard matrices \(A\) and \(B\) of \(T\) and \(U\), respectively

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