Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there exists some vectorin V that can be written as a nontrivial linear combinationof other vectors in V.

Show that a set of vectors V (not containing the 0 vector)is linearly dependent if and only if there exists some vectorin V that can be written as a nontrivial linear combinationof other vectors in V.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter1: Matrices, Vectors, And Vector Calculus

Section: Chapter Questions

Problem 1.32P: Show that (2arr+2brr)dt=ar2+br2+const. where r is the vector from the origin to the point (x1, x2,...

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Question

Show that a set of vectors V (not containing the 0 vector)
is linearly dependent if and only if there exists some vector
in V that can be written as a nontrivial linear combination
of other vectors in V.

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