x? the A. transformation that maps into Use the 17. Let T: R² R2 be a linear 5 -[2] into [2] 3 fact that T is linear to find the images under T of 3u, 2v, and 3u + 2v. u: and maps v =
x? the A. transformation that maps into Use the 17. Let T: R² R2 be a linear 5 -[2] into [2] 3 fact that T is linear to find the images under T of 3u, 2v, and 3u + 2v. u: and maps v =
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
17
![-r X
- to
der
x?
the
A.
11. Let b
and let A be the matrix in Exercise 9. Is b in
the range of the linear transformation x Ax? Why or why
not?
12. Let b =
b in the range of the linear transformation x → Ax? Why or
why not?
In Exercises 13-16, use a rectangular coordinate system to plot
sili nedi xam
1
3
-1
4
U=
¹ = [2] ·v = [-²]₁
4
13. 7(x) = [
14. T(x) =
mation T. (Make a separate and reasonably large sketch for each
exercise.) Describe geometrically what T does to each vector x
in R2.
15. T(x) =
16. T(x) =
and let A be the matrix in Exercise 10. Is
U=
0
.5
0
X1
9][*2
5 X2
X1
x2
x = [0
[
¡][*]
][*]
X1
17. Let T: R2 R2 be a linear transformation that maps
int
Use the
-[2] into [²]
fact that T is linear to find the images under T of 3u, 2v, and
3u + 2v.
, and their images under the given transfor-
X1
9][*]
X2
-
30
and maps v =
P(t)
ter
(t
na](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F787e472b-3dcf-45d7-8670-005f90d3000b%2F762974d6-dd80-41ca-91a9-4c8338771fb0%2Fhncms8g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:-r X
- to
der
x?
the
A.
11. Let b
and let A be the matrix in Exercise 9. Is b in
the range of the linear transformation x Ax? Why or why
not?
12. Let b =
b in the range of the linear transformation x → Ax? Why or
why not?
In Exercises 13-16, use a rectangular coordinate system to plot
sili nedi xam
1
3
-1
4
U=
¹ = [2] ·v = [-²]₁
4
13. 7(x) = [
14. T(x) =
mation T. (Make a separate and reasonably large sketch for each
exercise.) Describe geometrically what T does to each vector x
in R2.
15. T(x) =
16. T(x) =
and let A be the matrix in Exercise 10. Is
U=
0
.5
0
X1
9][*2
5 X2
X1
x2
x = [0
[
¡][*]
][*]
X1
17. Let T: R2 R2 be a linear transformation that maps
int
Use the
-[2] into [²]
fact that T is linear to find the images under T of 3u, 2v, and
3u + 2v.
, and their images under the given transfor-
X1
9][*]
X2
-
30
and maps v =
P(t)
ter
(t
na
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