Three vectors v,, V2,andV3are given. If they are linearly independent, show this; otherwise, find a nontrivial linear combination of them that is equal to the zero vector.- 319-13V1 =V2223- 16.Select the correct answer below, and fill in the answer box(es) to complete your choice.O A. The vectors are linearly dependent, becauseV1 + ( ) v2 + V3 = 0.(Type integers or fractions.)B. The vectors are linearly independent. The augmented matrix [v, v2 V3 0j has an echelon form E =(Type an integer or simplified fraction for each matrix element.)which has only the trivial solution.

A set of vectors is said to be linearly dependent if at least one of the vectors in the set can be…

ree vectors v,, V2, and vz 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 3 v = V2 = V3 3 -1 lect the correct answer below, and fill in the answer box(es) to complete your choice. A. The vectors are linearly dependent, because (Ov, + (D v2 + v3 = 0.

ree vectors v,, V2, and vz 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 3 v = V2 = V3 3 -1 lect the correct answer below, and fill in the answer box(es) to complete your choice. A. The vectors are linearly dependent, because (Ov, + (D v2 + v3 = 0.

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
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
9-
1
3
V1 =
V2
2
2
3
- 1
6.
Select the correct answer below, and fill in the answer box(es) to complete your choice.
O A. The vectors are linearly dependent, because
V1 + ( ) v2 + V3 = 0.
(Type integers or fractions.)
B. The vectors are linearly independent. The augmented matrix [v, v2 V3 0j has an echelon form E =
(Type an integer or simplified fraction for each matrix element.)
which has only the trivial solution.

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