Three vectors V₁, V2, and v3 are given. If they are linearly independent, show this; otherwise, find a nontrivial linear combination of them that is equal to the zero vector. V1 = 3 0 -2 2 V₂ = 1 1 0 2 V3 = 5 - 1 -4 -6 Select the correct answer below, and fill in the answer box(es) to complete your choice. OA. The vectors are linearly independent. The augmented matrix [V₁ V2 V30] has an echelon form E= which has only the trivial solution. (Type an integer or simplified fraction for each matrix element.) OB. The vectors are linearly dependent, because (v₁ + ₂ + V3 = 0. (Type integers or fractions.)
Three vectors V₁, V2, and v3 are given. If they are linearly independent, show this; otherwise, find a nontrivial linear combination of them that is equal to the zero vector. V1 = 3 0 -2 2 V₂ = 1 1 0 2 V3 = 5 - 1 -4 -6 Select the correct answer below, and fill in the answer box(es) to complete your choice. OA. The vectors are linearly independent. The augmented matrix [V₁ V2 V30] has an echelon form E= which has only the trivial solution. (Type an integer or simplified fraction for each matrix element.) OB. The vectors are linearly dependent, because (v₁ + ₂ + V3 = 0. (Type integers or fractions.)
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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![Three vectors V₁, V2, and v3 are given. If they are linearly independent, show this; otherwise, find a nontrivial
linear combination of them that is equal to the zero vector.
V₁ =
3
0
-2
V₂
ew an example
1
1
0
2
8
V3
Select the correct answer below, and fill in the answer box(es) to complete your choice.
O A. The vectors are linearly independent. The augmented matrix [v₁ V2 V3 0] has an echelon form
E=, which has only the trivial solution.
(Type an integer or simplified fraction for each matrix element.)
5
OB. The vectors are linearly dependent, because (v₁+ (v₂ + V3 =0.
(Type integers or fractions.)
H
- 1
-4
-6
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PRE](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04750898-40b6-4507-9bb8-e18bccce9e61%2F7deeed5d-feef-4482-a195-edf992e0d136%2F5gozxa_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Three vectors V₁, V2, and v3 are given. If they are linearly independent, show this; otherwise, find a nontrivial
linear combination of them that is equal to the zero vector.
V₁ =
3
0
-2
V₂
ew an example
1
1
0
2
8
V3
Select the correct answer below, and fill in the answer box(es) to complete your choice.
O A. The vectors are linearly independent. The augmented matrix [v₁ V2 V3 0] has an echelon form
E=, which has only the trivial solution.
(Type an integer or simplified fraction for each matrix element.)
5
OB. The vectors are linearly dependent, because (v₁+ (v₂ + V3 =0.
(Type integers or fractions.)
H
- 1
-4
-6
Get more help.
(...)
|0|
L
±
√I
TU
Clear all
More
Check answer
7:48 PM
2/26/2024
A
X
PRE
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