Sejam \alpha e \beta bases ordenadas de \mathbb{R}^{3} tais que [I]_{\alpha}^{\beta}=\left[\begin{array}{ccc}1 & 1 & 0 \\\\ 0 & -1 & 1 \\\\ 1 & 0 & -1\end{array}\right].
(a) Seja u \in \mathbb{R}^{3} tal que [u]_{\beta}=\left[\begin{array}{l}1 \\\\ 2 \\\\ 3\end{array}\right]. Determine [u]_{\alpha}.
(b) Seja v \in \mathbb{R}^{3} tal que [v]_{\alpha}=\left[\begin{array}{l}1 \\\\ 2 \\\\ 3\end{array}\right]. Determine [v]_{\beta}.