1. Consider 1 -2 B = B' = 2 4 1 1 (a) Show that B and B' are bases of R³. 9. (b) Find the coordinate matrices of v = relative to the bases B and B'. -5 (c) Find the transition matrix PB→B'. (d) Verify that ( [x(v)]B = PB-B' [x(v)B]. %3D

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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Please do the number 1(a) math and give a short explanation of how you did it.
1. Consider
{[:] [} }
1
2
2
1
B =
B'
1
4
1
(a) Show that B and B' are bases of R³.
9
(b) Find the coordinate matrices of v =
relative to the bases B and B'.
-5
(c) Find the transition matrix PB¬B'.
(d) Verify that
[x(v)]B = PB¬B' [x(v)B].
Transcribed Image Text:1. Consider {[:] [} } 1 2 2 1 B = B' 1 4 1 (a) Show that B and B' are bases of R³. 9 (b) Find the coordinate matrices of v = relative to the bases B and B'. -5 (c) Find the transition matrix PB¬B'. (d) Verify that [x(v)]B = PB¬B' [x(v)B].
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