Introduction to mathematical programming
Introduction to mathematical programming
4th Edition
ISBN: 9780534359645
Author: Jeffrey B. Goldberg
Publisher: Cengage Learning
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Chapter 2.6, Problem 4P

Explanation of Solution

a.

Proof:

Consider a 1×1 matrix,

A=[a]

Then, det(A)=a

Now, we have

A=[a]

Then, we get

det(A)=a             =det(A)

Similarly consider a 3×3 matrix as given below:

A=[a     b     c0     d     e0     f   

Explanation of Solution

b.

Proof:

Let us consider a  2×2 matrix as given below:

A=[a     bc     d]

Then, we get det(A)=adbc

Now, we have

A=[a    -bc    -d]

Then, we get

det(A)=adbc             =det(A)

Similarly consider a 4×4 matrix as,

A=[a     b     c      d0     e      f      g0     h      0    �

Explanation of Solution

Generalize the results of part (a.) and (b.):

From part a.) and part b.), we conclude that

For any n×n matrix,

det(A)=det(

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