Solved: Finding Transition and Coordinate Matrices In
Chapter 4, Problem 4.71(choose chapter or problem)
In Exercises 69–72, (a) find the transition matrix from B to \(B^{\prime}\), (b) find the transition matrix from B to B, (c) verify that the two transition matrices are inverses of each other, and (d) find the coordinate matrix \([\mathbf{x}]_{B^{\prime}}\), given the coordinate matrix \([\mathbf{x}]_{B^{\prime}}\).
B = {(1, 0, 0), (1, 1, 0), (1, 1, 1)},
\(B^{\prime}=\{(0,0,1),(0,1,1),(1,1,1)\}\),
\([\mathbf{x}]_{B}=\left[\begin{array}{lll} -1 & 2 & -3\end{array}\right]^{T}\)
Text Transcription:
B^prime
[mathbf x]_B^prime
[mathbf x]_B^prime
B^prime ={(0,0,1),(0,1,1),(1,1,1)}
[mathbf x]_B =-1 & 2 & -3]^T
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