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Find the transition matrix from B to B'. B = {(0, –1, 1), (3, 4, –2), (-3, 0, 1)}, B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}

Find the transition matrix from B to B'. B = {(0, –1, 1), (3, 4, –2), (-3, 0, 1)}, B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)}

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Find the Transition Matrix from \(B\) to \(B'\).** Given the bases: \[ B = \{(0, -1, 1), (3, 4, -2), (-3, 0, 1)\} \] \[ B' = \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\} \] **Diagram Explanation:** The image depicts a 3x3 matrix with empty slots (represented by boxes) arranged in three rows and three columns. This matrix is intended to illustrate the concept of finding a transition matrix that converts coordinates from the basis \(B\) to the basis \(B'\). - Each row corresponds to a vector in basis \(B\). - The columns correspond to the vectors in basis \(B'\). - The arrows suggest that we need to determine how each vector in \(B\) can be represented or transformed in terms of the vectors in \(B'\). To fill in the matrix: 1. Express each vector in \(B\) as a linear combination of the vectors in \(B'\). 2. Place the coefficients of each linear combination into the respective row of the matrix. This transition matrix will allow transformation between two coordinate systems defined by the bases \(B\) and \(B'\).
Transcribed Image Text:**Find the Transition Matrix from \(B\) to \(B'\).** Given the bases: \[ B = \{(0, -1, 1), (3, 4, -2), (-3, 0, 1)\} \] \[ B' = \{(1, 0, 0), (0, 1, 0), (0, 0, 1)\} \] **Diagram Explanation:** The image depicts a 3x3 matrix with empty slots (represented by boxes) arranged in three rows and three columns. This matrix is intended to illustrate the concept of finding a transition matrix that converts coordinates from the basis \(B\) to the basis \(B'\). - Each row corresponds to a vector in basis \(B\). - The columns correspond to the vectors in basis \(B'\). - The arrows suggest that we need to determine how each vector in \(B\) can be represented or transformed in terms of the vectors in \(B'\). To fill in the matrix: 1. Express each vector in \(B\) as a linear combination of the vectors in \(B'\). 2. Place the coefficients of each linear combination into the respective row of the matrix. This transition matrix will allow transformation between two coordinate systems defined by the bases \(B\) and \(B'\).
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