Question 4.7.5: Finding a Transition Matrix Find the transition matrix from ...
Finding a Transition Matrix
Find the transition matrix from B to B´ for the following bases for R² .
B = {(-3, 2), (4, -2)} and B´ = {(-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 ] .Related Answered Questions
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