Let B={(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R³, and let A= 2 2 be the matrix for T: R³ → R³ relative to B. (a) Find the transition matrix P from B' to B. P= 000 000= [1] (b) Use the matrices P and A to find [♥], and [7(v)]g, where [V]=[0-1 1]. [V]B= [T(V)]B= (c) Find P-1 and A' (the matrix for T relative to B'). A'= 000 (d) Find [T(v)]. two ways. [T(v)] = P¹[T(v)] = [T(v)] = A'[♥] = 000 000: 11
Let B={(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R³, and let A= 2 2 be the matrix for T: R³ → R³ relative to B. (a) Find the transition matrix P from B' to B. P= 000 000= [1] (b) Use the matrices P and A to find [♥], and [7(v)]g, where [V]=[0-1 1]. [V]B= [T(V)]B= (c) Find P-1 and A' (the matrix for T relative to B'). A'= 000 (d) Find [T(v)]. two ways. [T(v)] = P¹[T(v)] = [T(v)] = A'[♥] = 000 000: 11
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 B = {(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)} be bases for R3, and let A = {(1/2, -1, -1/2),(-3/2,2,1/2),(5/2,1,1/2)}
![Let B={(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R³, and let
A=
2
2
be the matrix for T: R³ → R³ relative to B.
(a) Find the transition matrix P from B' to B.
P=
000
000=
[1]
(b) Use the matrices P and A to find [♥], and [7(v)]g, where
[V]=[0-1 1].
[V]B=
[T(V)]B=
(c) Find P-1 and A' (the matrix for T relative to B').
A'=
000
(d) Find [T(v)]. two ways.
[T(v)] = P¹[T(v)] =
[T(v)] = A'[♥] =
000 000:
11](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e303283-8045-4d81-bcb2-cabd4c10c125%2F95c0cba1-2597-4af9-89b3-8a08ab9eabcf%2Fzlfm69b_processed.png&w=3840&q=75)
Transcribed Image Text:Let B={(1, 1, 0), (0, 1, 1), (1, 0, 1)} and B' = {(1, 0, 0), (0, 1, 0), (0, 0, 1)) be bases for R³, and let
A=
2
2
be the matrix for T: R³ → R³ relative to B.
(a) Find the transition matrix P from B' to B.
P=
000
000=
[1]
(b) Use the matrices P and A to find [♥], and [7(v)]g, where
[V]=[0-1 1].
[V]B=
[T(V)]B=
(c) Find P-1 and A' (the matrix for T relative to B').
A'=
000
(d) Find [T(v)]. two ways.
[T(v)] = P¹[T(v)] =
[T(v)] = A'[♥] =
000 000:
11
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