= {(1,2), (-1, –1)}, B' = {(-4, 1), (0, 2)} be bases for R². %3D 2 1 Let A = be the matrix for T : R? → R? 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)]B where [v]g = [-1 4]". (c) Find P-1 and A' (the matrix for T relative to B').
= {(1,2), (-1, –1)}, B' = {(-4, 1), (0, 2)} be bases for R². %3D 2 1 Let A = be the matrix for T : R? → R? 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)]B where [v]g = [-1 4]". (c) Find P-1 and A' (the matrix for T relative to B').
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 B = {(1,2), (-1, –1)}, B' = {(-4, 1), (0, 2)} be bases for R?.
%3|
2 1
be the matrix for T: R? –→ R² relative to B.
0 -1
Let A =
(a) Find the transition matrix P from B' to B.
(b) Use the matrices P and A to find [v]B and [T(v)]B where [v]g = [-1 4]".
(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%2Ff57fbb07-e1bd-418f-9d01-1252f5b1cb71%2F5d499ce2-98bb-4128-afcc-45eccd683981%2Fdxe5sip_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let B = {(1,2), (-1, –1)}, B' = {(-4, 1), (0, 2)} be bases for R?.
%3|
2 1
be the matrix for T: R? –→ R² relative to B.
0 -1
Let A =
(a) Find the transition matrix P from B' to B.
(b) Use the matrices P and A to find [v]B and [T(v)]B where [v]g = [-1 4]".
(c) Find P-1 and A' (the matrix for T relative to B').
(d) Find [T(v)]B' two ways.
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