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

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

Compute the product BA of the matrices found in #5 and illustrate use of theorem that states: If \(T: R^{n} \rightarrow R^{m}\) and \(U: R^{m} \rightarrow R^{p}\) are linear transformations w/standard matrices \(A\) and \(B\), respectively, then the composition

UT: \(R^{n} \rightarrow R^{p}\) is also linear, and its standard matrix is \(B A \ldots \ldots\) by comparing this answer with the result of #4.

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