pose: is the linear transformation defined in the figure below. The figure shows where 7 maps 8 vectors va from the domain. With this limited information about what properties of " can be determined? Part 1: Finding eigenvectors using geometry Which of the eight vectors drawn in the domain are eigenvectors? Enter your answer as a comma separated list of vector names such as v1.2 Eigenvectors . Part 2 Finding eigenvalues using geometry For each eigenvector from Part 1, find and enter the corresponding eigenvalue. help (numbers) T(v₂) b. (v₂)-vs CT(vs)- va d.T(vy)- vy Part 3: Generalizing observations about eigenvectors to eigenspaces a Select all of the eigenvectors for the linear transformation 7. There may be more than one correct answer CA(,0) B. (0,0) DC7-(45,0) D. any nonzero vector parallel to the line-0 E any nonzero vector parallel to the liney-- F(0,400) G. any nonzero vector parallel to the ai CH (1.1) O any nonzero vector parallel to the line- 130 b. The set of all eigenvectors of the linear transformation * A (A(1,0) | eR) 08 (4(1.1) AR) CC. (A(0, 1) (AR) OD ((-1,3)AR) domain I with eigenvalue 1.5 together with the zero vector (0,0) is the eigenspace s When described in words, the set is select all that apply (W) Hot A the zero vector together with all vectors parallel to (0, 1) B. the zero vector together with all vectors parallel to the line y- C. the zero vector together with all vectors parallel to the a-a D. the zero vector together with all vectors parallel to (1,0) DE the zero vector together with all vectors parallel to (1, 1) OF. the zero vector together with all vectors parallel to the s-avis c. The set of all eigenvectors of the linear transformation Twith eigenvalue 0.5 together with the zero vector (0, 0) is the eigenspace Bes. When described in set notation the set as is select all that apply FOOT ((W) (3) codomain 1 148) [(y)
pose: is the linear transformation defined in the figure below. The figure shows where 7 maps 8 vectors va from the domain. With this limited information about what properties of " can be determined? Part 1: Finding eigenvectors using geometry Which of the eight vectors drawn in the domain are eigenvectors? Enter your answer as a comma separated list of vector names such as v1.2 Eigenvectors . Part 2 Finding eigenvalues using geometry For each eigenvector from Part 1, find and enter the corresponding eigenvalue. help (numbers) T(v₂) b. (v₂)-vs CT(vs)- va d.T(vy)- vy Part 3: Generalizing observations about eigenvectors to eigenspaces a Select all of the eigenvectors for the linear transformation 7. There may be more than one correct answer CA(,0) B. (0,0) DC7-(45,0) D. any nonzero vector parallel to the line-0 E any nonzero vector parallel to the liney-- F(0,400) G. any nonzero vector parallel to the ai CH (1.1) O any nonzero vector parallel to the line- 130 b. The set of all eigenvectors of the linear transformation * A (A(1,0) | eR) 08 (4(1.1) AR) CC. (A(0, 1) (AR) OD ((-1,3)AR) domain I with eigenvalue 1.5 together with the zero vector (0,0) is the eigenspace s When described in words, the set is select all that apply (W) Hot A the zero vector together with all vectors parallel to (0, 1) B. the zero vector together with all vectors parallel to the line y- C. the zero vector together with all vectors parallel to the a-a D. the zero vector together with all vectors parallel to (1,0) DE the zero vector together with all vectors parallel to (1, 1) OF. the zero vector together with all vectors parallel to the s-avis c. The set of all eigenvectors of the linear transformation Twith eigenvalue 0.5 together with the zero vector (0, 0) is the eigenspace Bes. When described in set notation the set as is select all that apply FOOT ((W) (3) codomain 1 148) [(y)
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
Transcribed Image Text:SupposeT: R² → R² is the linear transformation defined in the figure below. The figure shows where I maps 8 vectors v₁...va from the domain. With this limited information about 7, what properties of I can be determined?
Part 2: Finding eigenvalues using geometry
For each eigenvector from Part 1, find and enter the corresponding eigenvalue. help (numbers)
a. T(v₁)=
b. T(v₂)=
CT(vs) =
d. T(vy)=
V1
Vs
V₂
V7
Part 3: Generalizing observations about eigenvectors to eigenspaces
a. Select all of the eigenvectors for the linear transformation T. There may be more than one correct answer.
A. (TT, 0)
OB. (0,0)
OCT-(45,0)
7
6
A. the zero vector together with all vectors parallel to (0,1)
OB. the zero vector together with all vectors parallel to the line y --
OC. the zero vector together with all vectors parallel to the -axis
5
Part 1: Finding eigenvectors using geometry
Which of the eight vectors drawn in the domain are eigenvectors? Enter your answer as a comma separated list of vector names, such as v1,v2.
• Eigenvectors:
4
9
2
1
A. (k(1,0) | R}
ⒸB. (k(1,1) | k = R}
OC. (k(0, 1)
= R}
OD. (k(-1,1)
k = R}
H
---2
Fa
Fo
-8-7-6-5-4-3-2-1
y
0
7
6
5
9
T(VG)
2
1
****
I
---2
T(4)
1 2 3
domain
D. any nonzero vector parallel to the line - 0
E. any nonzero vector parallel to the line y --
ⒸF. (0,450)
G. any nonzero vector parallel to the z-axis
OH. (1,1)
1. any nonzero vector parallel to the line y-
J. 303
b. The set of all eigenvectors of the linear transformation I with eigenvalue 1.5 together with the zero vector (0,0) is the eigenspace Bs. When described in words, the set Bis is (select all that apply):
4 5 6 7 8
Fo
D. the zero vector together with all vectors parallel to (1,0)
E. the zero vector together with all vectors parallel to (1, 1)
OF. the zero vector together with all vectors parallel to the y-axis
c. The set of all eigenvectors of the linear transformation T with eigenvalue -0.5 together with the zero vector (0, 0) is the eigenspace B-05- When described in set notation, the set B-05 is (select all that apply)
T(v/)
y
-8-7-6-5-4-3-2-1
T(v3)
T(VU)
Thott M
"
T(v2)
1 2 3 4 5 6 7 8
codomain
A
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