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December 10th, 2016, 09:34 PM   #1
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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 $\displaystyle P_{B\rightarrow {B}'}$.
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December 11th, 2016, 01:34 PM   #2
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Originally Posted by mosvas View Post
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 $\displaystyle P_{B\rightarrow {B}'}$.
Write it out as a matrix equation:
$\displaystyle v_1 = 12 u_1 + 2 u_2$

$\displaystyle v_2 = u_1 - 4 u_2$

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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