Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 2.5, Problem 8P

Explanation of Solution

a.

Inverse of the given matrix:

We know that for any square matrix A,

A1A=I

Therefore, we have,

(100B)1(100B)=I

Hence, we get

Explanation of Solution

b.

Obtaining the inverse:

Suppose B' be the matrix obtained by doubling every entry in row 1 of any n×n matrix B.

Then we have,

B'=[2    0    00    1    0         0    0    1]B

Now, we have,

(B')1=([2    0    00    1    0         0    0    1]B)1

  

Explanation of Solution

c.

Obtaining the inverse:

Suppose B' be the matrix obtained by doubling every entry in column 1 of any n×n matrix B.

Then, we have,

B'=B[2    0    00    1    0         0    0    1]

Now, we have,

(B')1=(B[2    0    00    1    0         0    0    1])1

 

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