to dierob od In Exercises 13-16, use a rectangular coordinate system to plot 5 U= = [2].v=[-²], an 4 -1 shi nomi x3 OT mation T. (Make a separate and reasonably large sketch for each exercise.) Describe geometrically what T does to each vector x in R2. 13. T(x) = 0 - and their images under the given transfor- X1 [*] X2 SS
to dierob od In Exercises 13-16, use a rectangular coordinate system to plot 5 U= = [2].v=[-²], an 4 -1 shi nomi x3 OT mation T. (Make a separate and reasonably large sketch for each exercise.) Describe geometrically what T does to each vector x in R2. 13. T(x) = 0 - and their images under the given transfor- X1 [*] X2 SS
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
13
![T(v).
ector x
ique.
rder to
n order
= Ax?
into the
trix A.
-[1]
the range of the linear transformation x→ Ax? Why or why
not?
11. Let b =
12. Let b =
1
, and let A be the matrix in Exercise 9. Is b in
and let A be the matrix in Exercise 10. Is
b in the range of the linear transformation x →→ Ax? Why or
why not?
Braob
In Exercises 13-16, use a rectangular coordinate system to plot
shi nati
19 FEB
and their images under the given transfor-
U=
= [2] = [-2]₁
u=
mation T. (Make a separate and reasonably large sketch for each
exercise.) Describe geometrically what T does to each vector x
in R².
13. T(x) = 0
14. T(x) =
(x) = [5
X1
X2
X1
9][*2]
X2
15. T(x) =
>= [89][*]
16. T(x) =
>= [i
[8][*]
X1
10
17. Let T: R2 R2 be a linear transformation that maps
[] into [3]
Use the
X1
and maps v =
fact that T is linear to find the images under T of 3u, 2v, and
3u + 2v.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F787e472b-3dcf-45d7-8670-005f90d3000b%2Fa0921c91-1742-471c-87f2-488e194f37c7%2F8vtlem9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:T(v).
ector x
ique.
rder to
n order
= Ax?
into the
trix A.
-[1]
the range of the linear transformation x→ Ax? Why or why
not?
11. Let b =
12. Let b =
1
, and let A be the matrix in Exercise 9. Is b in
and let A be the matrix in Exercise 10. Is
b in the range of the linear transformation x →→ Ax? Why or
why not?
Braob
In Exercises 13-16, use a rectangular coordinate system to plot
shi nati
19 FEB
and their images under the given transfor-
U=
= [2] = [-2]₁
u=
mation T. (Make a separate and reasonably large sketch for each
exercise.) Describe geometrically what T does to each vector x
in R².
13. T(x) = 0
14. T(x) =
(x) = [5
X1
X2
X1
9][*2]
X2
15. T(x) =
>= [89][*]
16. T(x) =
>= [i
[8][*]
X1
10
17. Let T: R2 R2 be a linear transformation that maps
[] into [3]
Use the
X1
and maps v =
fact that T is linear to find the images under T of 3u, 2v, and
3u + 2v.
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