Let B = {(0, 1, 1), (1, 0, 1), (1, 1, 0)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let -1 5 A 1 2 be the matrix for T: R3 → R3 relative to B. (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [V]g and [7(V)]g, where [V]g = [1 -1 0j". [V]B [T(V)]B = m/N -/2 1/2
Let B = {(0, 1, 1), (1, 0, 1), (1, 1, 0)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let -1 5 A 1 2 be the matrix for T: R3 → R3 relative to B. (a) Find the transition matrix P from B' to B. P = (b) Use the matrices P and A to find [V]g and [7(V)]g, where [V]g = [1 -1 0j". [V]B [T(V)]B = m/N -/2 1/2
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
![(c) Find P-1 and A' (the matrix for T relative to B').
p-1 =
A' =
(d) Find [T(V)]g' two ways.
[T(V)]g = P-1[T(v)]g
[T(V)]g = A'[V]g =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3818a4a-1b2c-4beb-97f8-270b02643a39%2F685f8028-e1e1-498e-8c72-63a3e15645c1%2Fxe77igs_processed.png&w=3840&q=75)
Transcribed Image Text:(c) Find P-1 and A' (the matrix for T relative to B').
p-1 =
A' =
(d) Find [T(V)]g' two ways.
[T(V)]g = P-1[T(v)]g
[T(V)]g = A'[V]g =
![Let B = {(0, 1, 1), (1, 0, 1), (1, 1, 0)} and B' =
{(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let
3
1
-1
2
2
5
A =
1
1.
2
2
be the matrix for T: R3 → R3 relative to B.
(a) Find the transition matrix P from B' to B.
P =
(b) Use the matrices P and A to find [v]g and [7(V)]g, where
[V]g = [1 -1 oj".
[V]B =
[T(V)]B
2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd3818a4a-1b2c-4beb-97f8-270b02643a39%2F685f8028-e1e1-498e-8c72-63a3e15645c1%2Ff8ij9s_processed.png&w=3840&q=75)
Transcribed Image Text:Let B = {(0, 1, 1), (1, 0, 1), (1, 1, 0)} and B' =
{(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let
3
1
-1
2
2
5
A =
1
1.
2
2
be the matrix for T: R3 → R3 relative to B.
(a) Find the transition matrix P from B' to B.
P =
(b) Use the matrices P and A to find [v]g and [7(V)]g, where
[V]g = [1 -1 oj".
[V]B =
[T(V)]B
2.
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