1. Let T: R² → R2 be the linear transformation T[*]-[***] a) Find [T] where a is the standard basis for R². b) Let 6 be the basis consisting of X2 x2 -2 [3][7] for R2. Find the change of basis matrix from a to ß. c) Find the change of basis matrix from ß to a. d) Find [7]. e) Find [v]s for v=[²3] · f) Find [T(v)]. g) Use the result of part (f) to find T (v).
1. Let T: R² → R2 be the linear transformation T[*]-[***] a) Find [T] where a is the standard basis for R². b) Let 6 be the basis consisting of X2 x2 -2 [3][7] for R2. Find the change of basis matrix from a to ß. c) Find the change of basis matrix from ß to a. d) Find [7]. e) Find [v]s for v=[²3] · f) Find [T(v)]. g) Use the result of part (f) to find T (v).
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 Exercise 7, do the parts of Exercise 1 for the given linear transformation, bases, and
Please solve question #7, ONLY question #7. PLEASE write it on PAPER.
![1. Let T: R² → R2 be the linear transformation
+ x₂
[3]-[***]
T
X2
a) Find [7] where a is the standard basis for R².
b) Let 6 be the basis consisting of
1
[3][7]
-1
for R2. Find the change of basis matrix from a
to B.
c) Find the change of basis matrix from ß to a.
d) Find [7].
e) Find [v]s for
V=
<-2
f) Find [T(v)].
g) Use the result of part (f) to find T (v).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbfa44710-6742-4cf8-9a38-b63fd4325c9b%2Fba86d311-0d7a-404b-b18f-40aa96861b86%2F3tvgif_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Let T: R² → R2 be the linear transformation
+ x₂
[3]-[***]
T
X2
a) Find [7] where a is the standard basis for R².
b) Let 6 be the basis consisting of
1
[3][7]
-1
for R2. Find the change of basis matrix from a
to B.
c) Find the change of basis matrix from ß to a.
d) Find [7].
e) Find [v]s for
V=
<-2
f) Find [T(v)].
g) Use the result of part (f) to find T (v).
Transcribed Image Text:7. D: V→ V where V is the set of solutions to the
differential equation y" + y = 0; a the basis of V
consisting of sin x, cos x; ß the basis consisting of
sin x + cos x, sin x - cos x; v = 3 cos x - 2 sin x.
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