# Given V = R, and two bases: B and C and the coordinator [v]B a) Find the change of coordinates matrix PB rightarrow C. b) Find the coordinator [v]C.

Given V = R, and two bases: B and C and the coordinator [v]B a) Find the change of coordinates matrix $PB\to C.$ b) Find the coordinator [v]C.
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Fatema Sutton

a .$\left[\begin{array}{c}9\\ 2\end{array}\right]={\prec }_{1}\left[\begin{array}{c}2\\ 1\end{array}\right]+{\prec }_{2}\left[\begin{array}{c}-3\\ 1\end{array}\right]⇒2{\prec }_{1}+\left(-3\right){\prec }_{2}=9{\prec }_{1}+{\prec }_{2}=2⇒2{\prec }_{1}+2{\prec }_{2}=42{\prec }_{1}+-3{\prec }_{2}=9{\prec }_{2}=-1⇒{\prec }_{1}=3\left[\begin{array}{c}4\\ -3\end{array}\right]=B1\left[\begin{array}{c}2\\ 1\end{array}\right]+B2\left[\begin{array}{c}-3\\ 1\end{array}\right]⇒2B1-3B2=4B1+B2=-3⇒2B1+2B2=-62B1-3B2=4⇒B2=-2,B1=-1{P}_{B←C}=\left[\begin{array}{cc}{\prec }_{1}& B1\\ {\prec }_{2}& B2\end{array}\right]=\left[\begin{array}{cc}3& -1\\ -1& -2\end{array}\right]$

b.