Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 2.4, Problem 9P

Explanation of Solution

Showing linear dependency of vectors:

Consider the following set of vectors,

V={v1,v2,,vn}

If this system of vectors is linearly dependent, then we have,

c1v1+c2v2++cnvn=0

For not all ci=0.

Now for some vector vk in V we can write as given below:

c1v1+c2v2++ckvk++cnvn=0

This can be written as follows:

vk=1ck(c1v1+c2v2++ck1vk1+ck+1vk+1+cnvn)

Therefore, we can see that a vector can be written as non-trivial combination of other vectors

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