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

Find the transition matrix from B to B'. B = {(4, 0, –3), (0, -2, -1), (3, 1, 1)}, B' = {(1, 0, 0), (0, 1, 0), (0, o, 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 bases: - \( B = \{ (4, 0, -3), (0, -2, -1), (3, 1, 1) \} \) - \( B′ = \{ (1, 0, 0), (0, 1, 0), (0, 0, 1) \} \) The task is to find the transition matrix that changes coordinates from basis \( B \) to basis \( B' \). **Visual Explanation:** - There is a matrix with empty cells positioned as a 3x3 grid. Each cell of this grid corresponds to an entry in the transition matrix. - Green arrows are shown: vertical arrows coming from the top of the matrix, and horizontal arrows pointing from left to right into the matrix. These arrows indicate how elements from basis \( B \) map to the standard basis \( B′ \). The goal is to fill out the matrix by determining how each vector in \( B \) is a linear combination of vectors in \( B′ \). This results in a 3x3 matrix that represents the transformation.
Transcribed Image Text:**Find the Transition Matrix from B to B′** Given bases: - \( B = \{ (4, 0, -3), (0, -2, -1), (3, 1, 1) \} \) - \( B′ = \{ (1, 0, 0), (0, 1, 0), (0, 0, 1) \} \) The task is to find the transition matrix that changes coordinates from basis \( B \) to basis \( B' \). **Visual Explanation:** - There is a matrix with empty cells positioned as a 3x3 grid. Each cell of this grid corresponds to an entry in the transition matrix. - Green arrows are shown: vertical arrows coming from the top of the matrix, and horizontal arrows pointing from left to right into the matrix. These arrows indicate how elements from basis \( B \) map to the standard basis \( B′ \). The goal is to fill out the matrix by determining how each vector in \( B \) is a linear combination of vectors in \( B′ \). This results in a 3x3 matrix that represents the transformation.
Expert Solution
Step 1

It is given that B=4,0,-3,0,-2,-1,3,1,1  and B'=1,0,0,0,1,0,0,0,1.

Obtain the augmented matrix B'B:

B'B=1004030100-21001-3-11

 

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