Let 8 = {(1, 3), (-2,-2)} and 8' = {(-12, 0), (-4, 4)} be bases for R² 4 2 A - [83] be the matrix for 7: R² R² relative to B. (a) Find the transition matrix P from 8' to 8. P= ↓1
Let 8 = {(1, 3), (-2,-2)} and 8' = {(-12, 0), (-4, 4)} be bases for R² 4 2 A - [83] be the matrix for 7: R² R² relative to B. (a) Find the transition matrix P from 8' to 8. P= ↓1
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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Question
![Let 8 = {(1, 3), (-2,-2)} and 8 = {(-12, 0), (-4, 4)) be bases for R2, and let
4 2
A =
- [83]
03
be the matrix for T: R2 R² relative to 8.
(a) Find the transition matrix P from 8' to 8.
P=
↓↑
(b) Use the matrices P and A to find [v] and [7(v)]g, where
[v] = [4 -1]7.
[7(v)]B
(c) Find P-¹ and A' (the matrix for 7 relative to 8').
p-1=
↓1
-88-
A'=
↓↑
(d) Find [7(v)]g' two ways.
[7(v)] = P¹[7(v)]g
=
[7(v)]g¹ = A'[v]g' =
=
[v]8 =
=
↓↑
8
↓ ↑](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd496c25d-6621-40aa-914c-10320ef32b36%2F66143b13-4fa9-430d-8565-d35053556413%2F7h847cu_processed.png&w=3840&q=75)
Transcribed Image Text:Let 8 = {(1, 3), (-2,-2)} and 8 = {(-12, 0), (-4, 4)) be bases for R2, and let
4 2
A =
- [83]
03
be the matrix for T: R2 R² relative to 8.
(a) Find the transition matrix P from 8' to 8.
P=
↓↑
(b) Use the matrices P and A to find [v] and [7(v)]g, where
[v] = [4 -1]7.
[7(v)]B
(c) Find P-¹ and A' (the matrix for 7 relative to 8').
p-1=
↓1
-88-
A'=
↓↑
(d) Find [7(v)]g' two ways.
[7(v)] = P¹[7(v)]g
=
[7(v)]g¹ = A'[v]g' =
=
[v]8 =
=
↓↑
8
↓ ↑
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