Example Let B = {(1,1,0), (1, -1, 0), (0, 0, 1)} and B' = {(1,0,0), (1,1,0), (-1,0,-1)}. Then B and B' are all bases for $R^3$. Find the transition matrix $P_{B \to B'}$. $P_{B \to B'} = \begin{bmatrix} 0 & 2 & -1 \ 1 & -1 & 0 \ 0 & 0 & -1 \end{bmatrix}$. Find $[(2,0,3)]_{B'}$ using the transition matrix.
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To find the transition matrix P, we need to express the basis B' in terms of the basis B. We can do this by writing each vector in B' as a linear combination of the vectors in B. The first vector in B' is 1. We can express 1 as a linear combination of the Show more…
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