Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
Expert Solution & Answer
Chapter 2.4, Problem 1P

Explanation of Solution

Determining the dependency of the given sets of vectors:

Consider the given sets of vectors,

V={[1 0 1], [1 2 1], [2 2 2]}

A matrix A is formed as given below; whose rows are the above given vectors:

A=[1 0 11 2 12 2 2]

The Gauss-Jordan method is applied to find the dependency of the above given sets of vectors.

Exchange row 3 and row 1, then the following matrix is obtained,

[2 2 21 2 11 0 1]

Multiply row 1 with 0.5, then the following matrix is obtained,

[1 1 11 2 11 0 1]

Now, replace row 2 by (row 2 – row 1), then the following matrix is obtained,

[1 1 10

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