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].
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].
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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Do the number 1(c) math and after that give a short explanation as a comment 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].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F89b773d6-6f0c-43c5-8497-4ca911f769a7%2Fad557a1e-56d8-45db-bada-3cb67b78b825%2Fo9p9f3_processed.jpeg&w=3840&q=75)
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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