$$ CHALLENGE Activity 6.3.2: Change of coordinates matrices. Jump to level 1 Given the following bases for $\mathbb{R}^{2}$, find $\underset{\mathcal{C} \leftarrow \mathcal{B}} P]$, the change of coordinates matrix from $\mathcal[B]$ to $\mathcal[C]$. \begin{array}{1) \mathcal[B)=\left\{\left|\begin{arrayHl} -5 -3 \end{array} ight], \left\begin{array}{1} 29 12 \end{array} ight] ight\} \quad \mathcal {C}=\left\{\left|\begin{array}1} 2 \end{array} ight], \left\begin{array}{1} 5 21 1 6 \end{array} ight] ight\} \underset{\mathcal{C} \leftarrow \mathcal{B} HP)=\left\begin{array}{11} operatorname[Ex:} \mathbf {1} What{\mathbf {v}} & What{\mathbf {v}} What{\mathbf {v}} & That [\mathbf {r}} \end{array} ight] {\text { If i\mathbf {v}{\mathcal{B}}=\left[\begin{array}{1} 1 \end{array} ight), \text { then }[\mathbf {v}b_{\mathcal{C}}={ \text { If } [ \mathbf {v} _{ \mathcal (B]} =[ \begin{array} {1} {6} \end{array} ], \text { then } [ \mathbf {v}]-{ \mathcal {C} } = [\begin{array} {\operatorname[Ex: 3) What{\mathbf {v}}}{\hat{\mathbf {v}}}] \end{array}) \end{array) $$ \begin{tabular}{111111111111 Thline 1 & 2 & $\mathbf {3}$ & 4 & 5 1 Whline Vend{tabular) SP.SD.3011