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.)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter8: Applications Of Trigonometry
Section8.4: The Dot Product
Problem 16E
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