Question: Consider the linear transformation \(L: R^{3} \rightarrow R^{3}\) given by:

1. What is the matrix of \(L\) with respect to the standard basis \(S: e_{1}, e_{2}, e_{3}\) of \(R^{3} ?\)
2. Consider the basis \(T: u_{1}=\left[\begin{array}{l}1 \\ 1 \\ 0\end{array}\right], u_{2}=\left[\begin{array}{l}1 \\ 0 \\ 1\end{array}\right], u_{3}=\left[\begin{array}{l}0 \\ 1 \\ 1\end{array}\right]\).
   What is the transition matrix from \(T\) to \(S\) ?
3. What is the matrix of \(L\) with respect to the basis \(T\) ?

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