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. 2 -⠀ V3 = 9 V₁0 V₂ = -9 2 3 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 independent. The augmented matrix [V₁ V₂ V3 0] has an echelon form E = the trivial solution. (Type an integer or simplified fraction for each matrix element.) OB. The vectors V₁, V₂, and v3 are linearly dependent, because 3v₁ + ( )√₂ + ( ) √3 = 0 (Type integers or fractions.) V3 0. which has only

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter1: Vectors
Section1.2: Length And Angle: The Dot Product
Problem 17EQ
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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 =
2
HH
V2 - 9
9
1
2
3
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 independent. The augmented matrix [V₁ V₂ V3 0] has an echelon form E =
the trivial solution.
(Type an integer or simplified fraction for each matrix element.)
+
B. The vectors V₁, V2, and v3 are linearly dependent, because 3v₁
(Type integers or fractions.)
v₂ + ( ) v₂ = 0.
which has only
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 = 2 HH V2 - 9 9 1 2 3 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 independent. The augmented matrix [V₁ V₂ V3 0] has an echelon form E = the trivial solution. (Type an integer or simplified fraction for each matrix element.) + B. The vectors V₁, V2, and v3 are linearly dependent, because 3v₁ (Type integers or fractions.) v₂ + ( ) v₂ = 0. which has only
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