December 10th, 2016, 09:34 PM  #1 
Newbie Joined: Dec 2016 From: Natal  Brazil Posts: 10 Thanks: 0  Transition matrix
Let $\displaystyle B =$ {$\displaystyle u_{1}, u_{2}$} and $\displaystyle {B}' = ${$\displaystyle v_{1}, v_{2}$} Two bases of any vector space $\displaystyle V$ any. If $\displaystyle v_{1} = 12u_{1} + 2u_{2}$ and $\displaystyle v_{2} = u_{1}  4u_{2}$. Get the transition matrix $\displaystyle P_{B\rightarrow {B}'}$.

December 11th, 2016, 01:34 PM  #2  
Math Team Joined: May 2013 From: The Astral plane Posts: 1,665 Thanks: 655 Math Focus: Wibbly wobbly timeywimey stuff.  Quote:
$\displaystyle v_1 = 12 u_1 + 2 u_2$ $\displaystyle v_2 = u_1  4 u_2$ Then $\displaystyle \left ( \begin{matrix} v_1 \\ v_2 \end{matrix} \right ) = \left ( \begin{matrix} 12 & 2 \\ 1 & 4 \end{matrix} \right ) \cdot \left ( \begin{matrix} u_1 \\ u_2 \end{matrix} \right ) $ Dan  

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