Question 4.7.5: Finding a Transition Matrix Find the transition matrix from ...

Finding a Transition Matrix

Find the transition matrix from B to for the following bases for R² .

B = {(-3, 2), (4, -2)}  and  = {(-1, 2), (2, -2)}

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Begin by forming the matrix

[B´   B] = \left [ \begin{matrix} -1 & 2 & -3 & 4 \\ 2 & -2 & 2 & -2 \end{matrix} \right ]

and use Gauss-Jordan elimination to obtain the transition matrix P^{-1} from B to B´:

[I_2   P^{-1}] = \left [ \begin{matrix} 1 & 0 & -1 & 2 \\ 0 & 1 & -2 & 3 \end{matrix} \right ].

So, you have

P^{-1} = \left [ \begin{matrix} -1 & 2 \\ -2 & 3 \end{matrix} \right ] .

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