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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. 1 V1 = 3 3 3 V2 = -5 , V3 = -7 12 14 ... 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 3v₁ + ( ) 2 + ( ) V3 = 0. (Type integers or fractions.) B. The vectors V1, V2, and V3 are linearly independent. The augmented matrix [V1 V2 V30] has an echelon form E = solution. which has only the trivial (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 V1 = 3 3 3 V2 = -5 , V3 = -7 12 14 ... 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 3v₁ + ( ) 2 + ( ) V3 = 0. (Type integers or fractions.) B. The vectors V1, V2, and V3 are linearly independent. The augmented matrix [V1 V2 V30] has an echelon form E = solution. which has only the trivial (Type an integer or simplified fraction for each matrix element.)

Advanced Engineering Mathematics
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. 1 V1 = 3 3 3 V2 = -5 , V3 = -7 12 14 ... 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 3v₁ + ( ) 2 + ( ) V3 = 0. (Type integers or fractions.) B. The vectors V1, V2, and V3 are linearly independent. The augmented matrix [V1 V2 V30] has an echelon form E = solution. which has only the trivial (Type an integer or simplified fraction for each matrix element.)
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 V1 = 3 3 3 V2 = -5 , V3 = -7 12 14 ... 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 3v₁ + ( ) 2 + ( ) V3 = 0. (Type integers or fractions.) B. The vectors V1, V2, and V3 are linearly independent. The augmented matrix [V1 V2 V30] has an echelon form E = solution. which has only the trivial (Type an integer or simplified fraction for each matrix element.)
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