1.) Let B {(1,1), (-2,3)}, and B' = {(1,-1), (0,1)} be bases for R?, and let A = | [3 21 4] Lo be the matrix for T: R2 → R² relative to B. a.) Find the transition matrix P from B' to B. b.) Use the matrices P and A to find [v]B and [T(v)]g where [v]p = [1 – 3]" c.) Find P-1 and A' (the matrix for T relative to B' d.) Find [T(v)]B, two ways.
1.) Let B {(1,1), (-2,3)}, and B' = {(1,-1), (0,1)} be bases for R?, and let A = | [3 21 4] Lo be the matrix for T: R2 → R² relative to B. a.) Find the transition matrix P from B' to B. b.) Use the matrices P and A to find [v]B and [T(v)]g where [v]p = [1 – 3]" c.) Find P-1 and A' (the matrix for T relative to B' d.) Find [T(v)]B, two ways.
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
In terms of
![1.) Let B
{(1,1), (–2,3)}, and B' = {(1,–1), (0,1)} be bases for R?, and let
[3 21
А
A =
Lo 4]
be the matrix for T: R2 → R² relative to B.
a.) Find the transition matrix P from B' to B.
b.) Use the matrices P and A to find [v]g and [T(v)]g where [v]p = [1 – 3]"
c.) Find P-1 and A' (the matrix for T relative to B'
d.) Find [T(v)]B, two ways.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd84c1829-b5be-42b1-ba72-3bae7a546286%2Ffe1899ff-f9a3-4388-aac7-025df2233f4f%2Fozs8ops_processed.png&w=3840&q=75)
Transcribed Image Text:1.) Let B
{(1,1), (–2,3)}, and B' = {(1,–1), (0,1)} be bases for R?, and let
[3 21
А
A =
Lo 4]
be the matrix for T: R2 → R² relative to B.
a.) Find the transition matrix P from B' to B.
b.) Use the matrices P and A to find [v]g and [T(v)]g where [v]p = [1 – 3]"
c.) Find P-1 and A' (the matrix for T relative to B'
d.) Find [T(v)]B, two ways.
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