Theorem: If P is the transition matrix from a basis B' to a basis B, then P is invertible and the transition matrix from B' to B is given by P-¹ and this can be found using Gauss-Jordan elimination as follows [B' | B] -> [P-¹]. Use the theorem above to find the transition matrix P(-¹) from B to B' where B={(1,0),(1,-1)} and B'={(1,1),(1,-1)}. From the previous problem question, find the coordinates with respect to B' of [v] B = [2,-2]. Simply find a,b such that [v]_B'=[a,b]¹. Show complete solutions.
Theorem: If P is the transition matrix from a basis B' to a basis B, then P is invertible and the transition matrix from B' to B is given by P-¹ and this can be found using Gauss-Jordan elimination as follows [B' | B] -> [P-¹]. Use the theorem above to find the transition matrix P(-¹) from B to B' where B={(1,0),(1,-1)} and B'={(1,1),(1,-1)}. From the previous problem question, find the coordinates with respect to B' of [v] B = [2,-2]. Simply find a,b such that [v]_B'=[a,b]¹. Show complete solutions.
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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![Theorem:
If P is the transition matrix from a basis B' to a basis B, then P is
invertible and the transition matrix from B' to B is given by P-¹ and this
can be found using Gauss-Jordan elimination as follows
[B' | B] -> [1 P-¹].
Use the theorem above to find the transition matrix P{-1} from
B to B' where B={(1,0),(1,-1)} and B'={(1,1),(1,-1)}.
From the previous problem question, find the coordinates with respect
to B' of [v] B = [2,-2]. Simply find a,b such that [v]_B'=[a,b]¹.
Show complete solutions.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49f3e251-119a-43e6-ab17-f6943d74a44f%2F5d405033-ad1b-47c0-9d59-bd76cbf4e25b%2Ffals74e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Theorem:
If P is the transition matrix from a basis B' to a basis B, then P is
invertible and the transition matrix from B' to B is given by P-¹ and this
can be found using Gauss-Jordan elimination as follows
[B' | B] -> [1 P-¹].
Use the theorem above to find the transition matrix P{-1} from
B to B' where B={(1,0),(1,-1)} and B'={(1,1),(1,-1)}.
From the previous problem question, find the coordinates with respect
to B' of [v] B = [2,-2]. Simply find a,b such that [v]_B'=[a,b]¹.
Show complete solutions.
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