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. - 3 - 1 - 3 - 3 1 V3 = V, = -2 2 2 -2 Select the correct answer below, and fill in the answer box(es) to complete your choice. O A. 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.) B. The vectors are linearly dependent, because () v, + (v2 + v3 = 0. (Type integers or fractions.)

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. - 3 - 1 - 3 - 3 1 V3 = V, = -2 2 2 -2 Select the correct answer below, and fill in the answer box(es) to complete your choice. O A. 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.) B. The vectors are linearly dependent, because () v, + (v2 + v3 = 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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Question

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.
- 3
- 1
- 3
- 3
V, =
1
V3 =
-2
2
2
Select the correct answer below, and fill in the answer box(es) to complete your choice.
O A. 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.)
O B. The vectors are linearly dependent, because ()v, + (Ov2 + v3 = 0.
(Type integers or fractions.)

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