# Transition Matrix

by Laney5
Tags: matrix, transition
 P: 5 Im trying to figure out how to do this question. This is an example in the book i have. Im not sure how they got the answer. Here is the example from the book: Find the Transition Matrix P from the basis B={t+1, 2t, t-1} to B'={4t$$^{2}$$-6t, 2t$$^{2}$$-2, 4t} for the space R[t]. A little computataion shows that 4t$$^{2}$$-6t:(-3, 2, -3), 2t$$^{2}$$-2: (-1, 1, 1) and 4t:(2, 0, 2). Therefore $$P=\left(\begin{array}{ccc}-3 & -1 & 2 \\ 2 & 1 & 0\\ -3 & 1 & 2\end{array}\right)$$ I'd like to know how they found 4t$$^{2}$$-6t to be(-3, 2, -3), 2t$$^{2}$$-2 to be (-1, 1, 1) and 4t to be(2, 0, 2). Any help is apprectated.