Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 2.1, Problem 3P

Explanation of Solution

Proving matrix multiplication is associative:

Suppose that there are three matrices A, B, and C such that matrix A has elements aij, matrix B has elements bij, and matrix C has elements cij.

The product BC is defined because the columns of B and rows of C are same.

Suppose D=BC. Then, the element of D is of the form given below:

dik=jbijcjk

The product AD is defined because the columns of A and rows of D are same.

Suppose E=AD. Then, the element of E is of the form given below:

elk=kalk(jbijcjk)..........(1)

Therefore, the matrix E=A(BC) have the elements elk

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