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)
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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,...
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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' =
↓ ↑
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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