Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8¹ = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R², and let be the matrix for 7: R³ R³ relative to 8. (a) Find the transition matrix P from B' to 8. U 1 -1 -888 0 x (b) Use the matrices P and A to find [v]g and [7(v)]g, where [v], [-1 1 0] ↓↑ [7(v)] = 8 ↓↑ (c) Find A and A' (the matrix for 7 relative to 8). p-1= A'= (d) Find [7(v)]g two ways. [7(v)] = P¹[7(v)] = [7(v)] = A'[v] = [v] = 000-000-
Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8¹ = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R², and let be the matrix for 7: R³ R³ relative to 8. (a) Find the transition matrix P from B' to 8. U 1 -1 -888 0 x (b) Use the matrices P and A to find [v]g and [7(v)]g, where [v], [-1 1 0] ↓↑ [7(v)] = 8 ↓↑ (c) Find A and A' (the matrix for 7 relative to 8). p-1= A'= (d) Find [7(v)]g two ways. [7(v)] = P¹[7(v)] = [7(v)] = A'[v] = [v] = 000-000-
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8¹ = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R², and let
be the matrix for 7: R³ R³ relative to 8.
(a) Find the transition matrix P from B' to 8.
U
1
-1
-888
0
x
(b) Use the matrices P and A to find [v]g and [7(v)]g, where
[v], [-1 1 0]
↓↑
[7(v)] =
8
↓↑
(c) Find A and A' (the matrix for 7 relative to 8).
p-1=
A'=
(d) Find [7(v)]g two ways.
[7(v)] = P¹[7(v)] =
[7(v)] = A'[v] =
[v] =
000-000-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd496c25d-6621-40aa-914c-10320ef32b36%2Ff27b1f97-a9fe-4906-af4f-7609a2637c53%2Foo6295e_processed.png&w=3840&q=75)
Transcribed Image Text:Let 8 = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and 8¹ = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R², and let
be the matrix for 7: R³ R³ relative to 8.
(a) Find the transition matrix P from B' to 8.
U
1
-1
-888
0
x
(b) Use the matrices P and A to find [v]g and [7(v)]g, where
[v], [-1 1 0]
↓↑
[7(v)] =
8
↓↑
(c) Find A and A' (the matrix for 7 relative to 8).
p-1=
A'=
(d) Find [7(v)]g two ways.
[7(v)] = P¹[7(v)] =
[7(v)] = A'[v] =
[v] =
000-000-
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