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, Problem 21RP

Explanation of Solution

Infinite number of solutions:

Consider the following linear system,

[x1  x2    xn]=[x1  x2    xn]P

Where P is as follows:

P=[p11     p12    p1np21    p22     p2n                 pn1    pn2     pnn]

This system can be written as given below:

[x1  x2    xn][PI]=0

Therefore, we have,

[PI]=[p11-1     p12          p1np21      p22-1        p2n                         pn1      pn2         pnn1]

We know that the transpose of the matrix does not affect the rank of the matrix.

Therefore, we get

[PI]T=[p11-1     p21          pn1p12      p22-1        pn2                         p1n      p2n         pnn1]

Adding all the rows in the last row will give

[P&

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