Let V₁ =1E-0-0-0-V3 =7-11=and V₁ =-51. Determine whether or not the four vectors listed above are linearly independent or linearly dependent.V₁+ V₂+ V3+ V₁=0If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds.

Answered: Let V₁ = ? V₂ == 3 6 -11 and V4= -3 1.…

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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Let V₁ =
1
E-0-0-0-
V3 =
7
-11
=
and V₁ =
-5
1. Determine whether or not the four vectors listed above are linearly independent or linearly dependent.
V₁+ V₂+ V3+ V₁=0
If they are linearly dependent, determine a non-trivial linear relation - (a non-trivial relation is three numbers which are not all three zero.) Otherwise, if the vectors are linearly independent, enter 0's for the coefficients, since that relationship always holds.

Expert Solution

Step 1

Introduction:

Let $A = (v 1, v 2, . . ., v r)$ represent a group of vectors from $R^{n}$ . A is said to be linearly dependent if $r > 2$ and at least one of the vectors in A can be expressed as a linear combination of the others. The purpose of this description is straightforward: One or more of the vectors are linearly dependent on one another. On the other hand, A is considered to be a linearly independent set if there isn't a vector in it. The phrase "the vectors are linearly dependent (or independent)" is also frequently used in place of the phrase "the set comprising these vectors is linearly dependent (or independent)."