Operations Research: Applications and Algorithms
Operations Research: Applications and Algorithms
4th Edition
ISBN: 9780357907818
Author: WINSTON
Publisher: Cengage Learning US
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Chapter 2.1, Problem 4P

Explanation of Solution

Proving (AB)T=BTAT:

Consider a matrix A of order m×n and another matrix B of order n×k, then the product AB is defined because the columns in A are equal to the rows in B.

Thus, the matrix AB will be of the order m×k.

The matrix A has elements ali and the matrix B has elements bij.

Then, the element of D=AB will be of the form given below:

dlj=i=1nalibij......(1)

Transpose of this matrix is (AB)T. The matrix is of the order k×m.

And the element of the matrix DT=(AB)T is of the form djl.

Now the transpose of the matrix B is BT and it will be of the order k×n.

The element in BT is of the form bji

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