Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R², and let 20 --[9] A 43 be the matrix for T: R² R² relative to B. (a) Find the transition matrix P from B' to B.
Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R², and let 20 --[9] A 43 be the matrix for T: R² R² relative to B. (a) Find the transition matrix P from B' to B.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
Related questions
Question
![Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let
20
+= [3₂9]
4
be the matrix for T: R² R² relative to B.
(a) Find the transition matrix P from B' to B.
6
4
←
P =
9
4
(b) Use the matrices P and A to find [v] and [T(v)]g, where
[v] = [4 -1].
5
[v] B =
[T(v)] B =
X
(c) Find P-¹ and A' (the matrix for T relative to B').
p-1 =
189:
A
A' =
↓ ↑](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1492c013-9918-41af-bd70-95c7cddfa2a1%2Ff4fc667d-5b76-4090-8e06-bec2f579b0a9%2Fvaav0vo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let B = {(1, 3), (-2,-2)} and B' = {(-12, 0), (-4,4)} be bases for R2, and let
20
+= [3₂9]
4
be the matrix for T: R² R² relative to B.
(a) Find the transition matrix P from B' to B.
6
4
←
P =
9
4
(b) Use the matrices P and A to find [v] and [T(v)]g, where
[v] = [4 -1].
5
[v] B =
[T(v)] B =
X
(c) Find P-¹ and A' (the matrix for T relative to B').
p-1 =
189:
A
A' =
↓ ↑
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