-1 2 A = 2 1. pe the matrix for T: R3 - R3 relative to B. (a) Find the transition matrix P from B' to B. P= 2.
-1 2 A = 2 1. pe the matrix for T: R3 - R3 relative to B. (a) Find the transition matrix P from B' to B. P= 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
5) PLEASE ANSWER EACH QUESTION, THANKS.
![Let B = {(0, 1, 1), (1, 1, 0), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R³, and let
A =
2
1
be the matrix for T: R3 - R relative to B.
(a) Find the transition matrix P from B' to B.
P=
(b) Use the matrices P and A to find [v]a and [T(v)]3, where
[v]g = [0 1 -1]".
|-1
[v]g =
|-2
3
[T(v)]g =
(c) Find P-1 and A' (the matrix for T relative to B').
p-1=
A' =
(d) Find [T(v)]' two ways.
[T(v)]g = P-[T(v)]; =
[T(v)]g = A'[v]g' =
A mIN inN -~](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc1f02723-d9e1-4704-83ab-f90dc08f102d%2Ff82d5833-999b-4384-b2b7-783d09457ecd%2F29owcsn_processed.png&w=3840&q=75)
Transcribed Image Text:Let B = {(0, 1, 1), (1, 1, 0), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R³, and let
A =
2
1
be the matrix for T: R3 - R relative to B.
(a) Find the transition matrix P from B' to B.
P=
(b) Use the matrices P and A to find [v]a and [T(v)]3, where
[v]g = [0 1 -1]".
|-1
[v]g =
|-2
3
[T(v)]g =
(c) Find P-1 and A' (the matrix for T relative to B').
p-1=
A' =
(d) Find [T(v)]' two ways.
[T(v)]g = P-[T(v)]; =
[T(v)]g = A'[v]g' =
A mIN inN -~
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