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. DEHT- Select the correct answer below, and fill in the answer box(es) to complete your choice. A. The vectors are linearly independent. The augmented matrix [V1 V2 V30] has an echelon form E = the trivial solution. which has only (Type an integer or simplified fraction for each matrix element.) B. The vectors are linearly dependent, because 3√₁ + ( ) √2 + ( ) √3 = 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. DEHT- Select the correct answer below, and fill in the answer box(es) to complete your choice. A. The vectors are linearly independent. The augmented matrix [V1 V2 V30] has an echelon form E = the trivial solution. which has only (Type an integer or simplified fraction for each matrix element.) B. The vectors are linearly dependent, because 3√₁ + ( ) √2 + ( ) √3 = 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.
DEHT-
Select the correct answer below, and fill in the answer box(es) to
complete your choice.
A. The vectors are linearly independent. The augmented matrix
[V1 V2 V30] has an echelon form E =
the trivial solution.
which has only
(Type an integer or simplified fraction for each matrix element.)
B. The vectors are linearly dependent, because
3√₁ + ( ) √2 + ( ) √3 = 0.
(Type integers or fractions.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1ae1bb18-ef65-433d-a0dc-aafdea4542d4%2F7a6b25d0-3ec3-4299-b333-9e1e43e45c18%2F8skfcny_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.
DEHT-
Select the correct answer below, and fill in the answer box(es) to
complete your choice.
A. The vectors are linearly independent. The augmented matrix
[V1 V2 V30] has an echelon form E =
the trivial solution.
which has only
(Type an integer or simplified fraction for each matrix element.)
B. The vectors are linearly dependent, because
3√₁ + ( ) √2 + ( ) √3 = 0.
(Type integers or fractions.)
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