Student Suite Cd-rom For Winston's Operations Research: Applications And Algorithms
Student Suite Cd-rom For Winston's Operations Research: Applications And Algorithms
4th Edition
ISBN: 9780534423551
Author: Wayne L. Winston
Publisher: Cengage Learning
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Chapter 2.5, Problem 2P

Explanation of Solution

Finding out the Inverse:

Consider the following matrix,

A=[1    0    14    1   -23    1   -1]

Suppose the inverse of this matrix is as follows:

A1=[e    f    gh    i    jk    l   m]

Then we have to solve the following equations,

[1    0    14    1   -23    1   -1][ehk]=[100]

[1    0    14    1   -23    1   -1][fil]=[010]

[1    0    14    1   -23    1   -1][gjm]=[001]

Hence, we get the augmented matrices respectively as follows:

A|b=(101141203110)

B|d=(101041213110)

C|v=(101041203111)

Now, apply Gauss – Jordan method.

Replacing row 2 by (row 2) – 4(row 1) of A|b, we get,

 A1|b1=(101101643110)

Replacing row 3 by (row 3) – 3(row 1) of A1|b1, we get,

A2|b2=(101101640143)

Replacing row 3 by (row 3 – row 2) of A2|b2, we get

A3|b3=(101101640021)

This gives us,

e+k=1h6k=4      k=12

Therefore, we get,

      e=12       h=1      k=12

Now, we solve for f, i and l

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