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 15RP

Explanation of Solution

a.

Existence of Inverse:

Consider the following matrix,

A=[a     0     0     00     b     0     00     0     c     00     0     0  &#

Explanation of Solution

b.

Finding the inverse of the given matrix:

Consider the following matrix,

A=[a     0     0     00     b     0     00     0     c     00     0     0     d]

Suppose the inverse of the matrix A is as follows:

A1=[e     0     0     00     f     0     00     0     g     00     0     0     h]

Then we have to solve the following equation

[a     0     0     00     b     0     00     0     c     00     0     0     d][e000]=[1000]

This gives us

e=1a

Also, we have

[a     0     0     00     b     0     00     0     c     00     0     0     d][0f00]=

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