Let B = {(1, 1, 1), (1, −1, 1), (0, 0, 1)}, B′= {(2, 2, 0), (0, 1, 1), (1, 0, 1)}, and [x]B′=[2 3 1]T . (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 from (a) and (b) are inverses of each other. (d) Find the coordinate matrix [x]B

Let B = {(1, 1, 1), (1, −1, 1), (0, 0, 1)}, B′= {(2, 2, 0), (0, 1, 1), (1, 0, 1)}, and [x]B′=[2 3 1]T . (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 from (a) and (b) are inverses of each other. (d) Find the coordinate matrix [x]B

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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Let B = {(1, 1, 1), (1, −1, 1), (0, 0, 1)}, B′= {(2, 2, 0), (0, 1, 1), (1, 0, 1)}, and [x]B′=[2 3 1]T .
(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 from (a) and (b) are inverses of each other.
(d) Find the coordinate matrix [x]B

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