B = {(7, 8, 4), (3, 4, 2), (6, 8, 5)}, B' = {(10, 3, 6), (3, 1, 2), (3, 1, 3)}, [x]B' = 1 2 −1 (a) Find the transition matrix from B to B'. P−1 = (b) Find the transition matrix from B' to B. P = (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 = Back
B = {(7, 8, 4), (3, 4, 2), (6, 8, 5)}, B' = {(10, 3, 6), (3, 1, 2), (3, 1, 3)}, [x]B' = 1 2 −1 (a) Find the transition matrix from B to B'. P−1 = (b) Find the transition matrix from B' to B. P = (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 = Back
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
B = {(7, 8, 4), (3, 4, 2), (6, 8, 5)}, B' = {(10, 3, 6), (3, 1, 2), (3, 1, 3)},
[x]B' =
|
|
|||
2 | ||||
−1 |
(a) Find the transition matrix from B to B'.
(b) Find the transition matrix from B' to B.
(c) Verify that the two transition matrices are inverses of each other.
(d) Find the coordinate matrix [x]B , given the coordinate matrix [x]B'.
P−1 = |
|
(b) Find the transition matrix from B' to B.
P = |
|
(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 = |
|
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