Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
Expert Solution & Answer
Book Icon
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

Blurred answer
Students have asked these similar questions
6. (Linear independence ): Is it true that if x; y; and z are linearly independent vectors overGF(q), then so are x + y; y + z, and z + x ?
Determine the value(s) of x so that the matrix below is the augmented matrixof an inconsistent linear system. x 1 5 5 -3 2
Bu = ƒ and Cu = f might be solvable even though B and C are singular. Show that every vector f = Bu has ƒ1 + ƒ2+ ……. +fn = 0. Physical meaning: the external forces balance. Linear algebra meaning: Bu = ƒ is solvable when ƒ is perpendicular to the all – ones column vector   e = (1, 1, 1, 1…) = ones (n, 1).
Knowledge Booster
Background pattern image
Similar questions
Recommended textbooks for you
Text book image
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole