Prove that if the set of vectors {ν1, . . . , νn} is linearly independent in V, then so is the list {ν1 − ν2,ν2 − ν3, ... ,νn−1 − νn, νn} obtained by subtracting from each vector (except the last one) the following vector

Prove that if the set of vectors {ν1, . . . , νn} is linearly independent in V, then so is the list {ν1 − ν2,ν2 − ν3, ... ,νn−1 − νn, νn} obtained by subtracting from each vector (except the last one) the following vector

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...

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Question

Prove that if the set of vectors {ν₁, . . . , ν_n} is linearly independent in V, then so is the list {ν₁ − ν₂,ν₂ − ν₃, ... ,ν_n−1 − ν_n, ν_n} obtained by subtracting from each vector (except the last one) the following vector.

Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.

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