Consider the following two ordered bases of $\mathbb{R}^{3}$: $$\begin{array}{lcl} \mathcal{B} & = & \lbrace \left<-1,1,-1\right>, \left<-1,2,-1\right>, \left<2,-2,1\right> \rbrace, \\ \mathcal{C} & = & \lbrace \left<0,1,-1\right>, \left<0,2,-1\right>, \left<1,-2,1\right> \rbrace. \end{array}$$

1. Find the change of basis matrix from the basis $\mathcal{B}$ to the basis $\mathcal{C}$.
   
   $\lbrack id \rbrack_{\mathcal{B}}^{\mathcal{C}} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$
   
   
2. Find the change of basis matrix from the basis $\mathcal{C}$ to the basis $\mathcal{B}$.
   
   $\lbrack id \rbrack_{\mathcal{C}}^{\mathcal{B}} =$ $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$