Consider the following. B = {(-20, -2, -4), (12, 1, 2), (-24, -2, -3)}, B' = {(7, -2, -2), (-3, 1, 1), (3, -1, 0)}, 1 [x]B' = 2 (a) Find the transition matrix from B to B'. p-1 = (b) Find the transition matrix from B' to B. P = 000 000
Consider the following. B = {(-20, -2, -4), (12, 1, 2), (-24, -2, -3)}, B' = {(7, -2, -2), (-3, 1, 1), (3, -1, 0)}, 1 [x]B' = 2 (a) Find the transition matrix from B to B'. p-1 = (b) Find the transition matrix from B' to B. P = 000 000
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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Question
![(c) Verify that the two transition matrices are inverses of each other.
PP-1 =
↓ ↑
(d) Find the coordinate matrix [x]B, given the coordinate matrix [x]B'.
[X]B =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7515da3-ce1f-46f4-afa5-a3c718ad7f99%2F029b6311-c7ac-42aa-870e-ccc112207aed%2Fa2tsh3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(c) Verify that the two transition matrices are inverses of each other.
PP-1 =
↓ ↑
(d) Find the coordinate matrix [x]B, given the coordinate matrix [x]B'.
[X]B =
![Consider the following.
B = {(-20, -2, -4), (12, 1, 2), (-24, -2, -3)}, B' = {(7, -2, -2), (-3, 1, 1), (3, -1, 0)},
1
1
2
-1
(a) Find the transition matrix from B to B'.
[x]B'
=
p-1 =
P =
↓ 1
(b) Find the transition matrix from B' to B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7515da3-ce1f-46f4-afa5-a3c718ad7f99%2F029b6311-c7ac-42aa-870e-ccc112207aed%2Foet6ym_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the following.
B = {(-20, -2, -4), (12, 1, 2), (-24, -2, -3)}, B' = {(7, -2, -2), (-3, 1, 1), (3, -1, 0)},
1
1
2
-1
(a) Find the transition matrix from B to B'.
[x]B'
=
p-1 =
P =
↓ 1
(b) Find the transition matrix from B' to B.
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Step 1: Define transition matrix from a basis to another basis
VIEWStep 2: Construct an augmented matrix
VIEWStep 3: Determine the required transition matrix from B to B'
VIEWStep 4: Determine the required transition matrix from B to B' using row operation
VIEWStep 5: Determine the required transition matrix from B' to B
VIEWStep 6: Determine the required transition matrix from B' to B
VIEWStep 7: Find the product of two transition matrix
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