Finding Transition and Coordinate Matrices In Exercises 4144, use a software program or

Chapter 4, Problem 41

(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 = {(4, 2, −4), (6, −5, −6), (2, −1, 8)},         \(B^{\prime}=\{(1, 0, 4), (4, 2, 8), (2, 5, −2)\}\), \([\mathbf{x}]_{B^{\prime}}=\left[\begin{array}{lll} 1 & -1 & 2 \end{array}\right]^{T}\)

Text Transcription:

B^prime

B^prime

[mathbf x]_B

[mathbf x]_B

B^prime ={(1, 0, 4), (4, 2, 8), (2, 5, −2)}

[mathbf x]_B^prime =[ 1 & -1 & 2 ]^T