Answer: Finding Transition and Coordinate Matrices In

Chapter 4, Problem 44

(choose chapter or problem)

In Exercises 41–44, use a software program or a graphing utility to (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, 9), (−9, 1, 1), (1, 9, −1)},         \(B^{\prime}=\{(3, 0, 3), (−3, 3, 0), (0, −3, 3)\}\), \([\mathbf{x}]_{B^{\prime}}=\left[\begin{array}{lll} -5 & -4 & 1 \end{array}\right]^{T}\)

Text Transcription:

B^prime

B^prime

[mathbf x]_B

[mathbf x]_B

B^prime ={(0, −1, −3), (−1, 3, −2), (−3, −2, 0)}

[mathbf x]_B^prime =[ -5 & -4 & 1 ]^T