Finding Transition and Coordinate Matrices In Exercises 3740, (a) find the transition
Chapter 4, Problem 40(choose chapter or problem)
In Exercises 37–40, (a) find the transition matrix from B to \(B^{\prime}\), (b) find the transition matrix from \(B^{\prime}\) to B, (c) verify that the two transition matrices are inverses of each other, and (d) find the coordinate matrix \([\mathbf{x}]_{B}\), given the coordinate matrix \([\mathbf{x}]_{B}\).
B = {(1, 1, 1), (1, −1, 1), (0, 0, 1)}, \(B^{\prime}=\{(2, 2, 0), (0, 1, 1), (1, 0, 1)\}\), \([\mathbf{x}]_{B^{\prime}}=\left[\begin{array}{r} 2 \\ 3 \\ 1 \end{array}\right]\)
Text Transcription:
B^prime
B^prime
[mathbf x]_B
[mathbf x]_B
B^prime ={(2, 2, 0), (0, 1, 1), (1, 0, 1)}
[mathbf x]_B^prime =[ 2 \\ 3 \\ 1 ]
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