et 8- ((1, 2), (-1,-1)) and 8- ((-4, 1), (0, 2)) be bases for R², and let A-83] А we 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]s and [7(v)le, where [v]-[-34). (vla- [T(V)]a- p-1. A'= x (c) Find P-1 and A' (the matrix for T relative to 8). X -1/4 12 1/8 10 -1/2 9/4 1/2 -1/2 x (d) Find (T(v)la two ways. [T()le-P¹[T(v)le- -5/2 19/4
et 8- ((1, 2), (-1,-1)) and 8- ((-4, 1), (0, 2)) be bases for R², and let A-83] А we 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]s and [7(v)le, where [v]-[-34). (vla- [T(V)]a- p-1. A'= x (c) Find P-1 and A' (the matrix for T relative to 8). X -1/4 12 1/8 10 -1/2 9/4 1/2 -1/2 x (d) Find (T(v)la two ways. [T()le-P¹[T(v)le- -5/2 19/4
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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![Let B ((1, 2), (-1, -1)) and 8 ((-4, 1), (0, 2)) be bases for R², and let
*-[83]
be the matrix for T: R² R² relative to B.
(a) Find the transition matrix P from 8' to 8.
P=
(b) Use the matrices P and A to find [v] and [7(v)le, where
[v]-[-3 4].
[v] =
[T(V)]=
p-1a
(c) Find p1 and A' (the matrix for T relative to 8).
A¹ =
X
-1/4
12
1/8
10
-1/2
-9/4
1/2
1/2
(d) Find (T(v)la two ways.
[T(V)le-P¹[T(v)le -
[T(v)]A[vle -
5/2
19/4
5/2
19/4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc17b884f-da2a-4651-8d85-b5edcc64f900%2Fd197375d-a33c-41d0-ba1a-431d40a99c11%2Fbk3pxdn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let B ((1, 2), (-1, -1)) and 8 ((-4, 1), (0, 2)) be bases for R², and let
*-[83]
be the matrix for T: R² R² relative to B.
(a) Find the transition matrix P from 8' to 8.
P=
(b) Use the matrices P and A to find [v] and [7(v)le, where
[v]-[-3 4].
[v] =
[T(V)]=
p-1a
(c) Find p1 and A' (the matrix for T relative to 8).
A¹ =
X
-1/4
12
1/8
10
-1/2
-9/4
1/2
1/2
(d) Find (T(v)la two ways.
[T(V)le-P¹[T(v)le -
[T(v)]A[vle -
5/2
19/4
5/2
19/4
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