(a) Find a subset of the set {(5,1, 2), (1, 3, 5), (7, 7, 12), (2, 1, 5)} that forms a basis, call it B', for R³ (b) Find the transition matrix PB→B' from B = {(1, 1, 1), (1, 2, 4), (0, 1, 2)} to B' (show important steps). (c) Compute the coordinate vector [w] B where w = (3, 5, 8) with respect to the standard basis. (d) Use PB→B' to find [W] B'.
(a) Find a subset of the set {(5,1, 2), (1, 3, 5), (7, 7, 12), (2, 1, 5)} that forms a basis, call it B', for R³ (b) Find the transition matrix PB→B' from B = {(1, 1, 1), (1, 2, 4), (0, 1, 2)} to B' (show important steps). (c) Compute the coordinate vector [w] B where w = (3, 5, 8) with respect to the standard basis. (d) Use PB→B' to find [W] B'.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.5: Basis And Dimension
Problem 66E
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Question
![(a) Find a subset of the set {(5, 1, 2), (1, 3, 5), (7, 7, 12), (2, 1, 5)} that forms a basis, call it B', for
R³
(b) Find the transition matrix PB→B' from B = {(1, 1, 1), (1, 2, 4), (0, 1, 2)} to B' (show important
steps).
(c) Compute the coordinate vector [w] B where w = (3, 5, 8) with respect to the standard basis.
(d) Use PB B' to find [W] B'.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92b3472e-ab59-40f2-b296-ac3727a4d9f3%2Fca294241-905a-4e7f-b8e0-1acb8f5f3af5%2Fpanrqsb_processed.png&w=3840&q=75)
Transcribed Image Text:(a) Find a subset of the set {(5, 1, 2), (1, 3, 5), (7, 7, 12), (2, 1, 5)} that forms a basis, call it B', for
R³
(b) Find the transition matrix PB→B' from B = {(1, 1, 1), (1, 2, 4), (0, 1, 2)} to B' (show important
steps).
(c) Compute the coordinate vector [w] B where w = (3, 5, 8) with respect to the standard basis.
(d) Use PB B' to find [W] B'.
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