Three vectors v,, v2, and va are given. If they are linearly independent, show this; otherwise, find a nontrivial linear combination of them that is equal to the zero vector. -6 V3 2 Select the correct answer below, and fill in the answer box(es) to complete your choice. O A. The vectors are linearly dependent, because (Dv, + ( v2 + V3 = 0. (Type integers or fractions.) O B. The vectors are linearly independent. The augmented matrix [v, v2 v3 01 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
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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.
- 3
1
- 6
V1
2
3
Select the correct answer below, and fill in the answer box(es) to complete your choice.
A. The vectors are linearly dependent, because
V1 + ( Dv2 +v3 = 0.
(Type integers or fractions.)
O B. The vectors are linearly independent. The augmented matrix [v, v, v3 0] has an echelon form E =
which has only the trivial solution.
(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. - 3 1 - 6 V1 2 3 Select the correct answer below, and fill in the answer box(es) to complete your choice. A. The vectors are linearly dependent, because V1 + ( Dv2 +v3 = 0. (Type integers or fractions.) O B. The vectors are linearly independent. The augmented matrix [v, v, 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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