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. 1 0 V2 1 7 -9 V3 6 AHAHA 14 - 5 9 Select the correct answer below, and fill in the answer box(es) to complete your choice. A. The vectors V₁, V2, and V3 are linearly dependent, because 2v₁ + ( ) V2 + ( ) √3 = 0. (Type integers or fractions.) B. The vectors V1, V2, and V3 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.)
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. 1 0 V2 1 7 -9 V3 6 AHAHA 14 - 5 9 Select the correct answer below, and fill in the answer box(es) to complete your choice. A. The vectors V₁, V2, and V3 are linearly dependent, because 2v₁ + ( ) V2 + ( ) √3 = 0. (Type integers or fractions.) B. The vectors V1, V2, and V3 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.)
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
![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.
1
0
V2
1
7
-9 V3
6
AHAHA
14
- 5
9
Select the correct answer below, and fill in the answer box(es) to
complete your choice.
A. The vectors V₁, V2, and V3 are linearly dependent, because
2v₁ + ( ) V2 + ( ) √3 = 0.
(Type integers or fractions.)
B. The vectors V1, V2, and V3 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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ae1bb18-ef65-433d-a0dc-aafdea4542d4%2F2ecd9020-b9c0-43e9-82ec-e9c385b0af9c%2Fg65g39h_processed.png&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.
1
0
V2
1
7
-9 V3
6
AHAHA
14
- 5
9
Select the correct answer below, and fill in the answer box(es) to
complete your choice.
A. The vectors V₁, V2, and V3 are linearly dependent, because
2v₁ + ( ) V2 + ( ) √3 = 0.
(Type integers or fractions.)
B. The vectors V1, V2, and V3 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.)
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