Chapter 4.2, Problem 31E

### Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426

Chapter
Section

### Finite Mathematics

7th Edition
Stefan Waner + 1 other
ISBN: 9781337280426
Textbook Problem

# Exercises 31–38 should be done in two ways: by hand and by using technology where possible.Let A = [ 0 − 1 0 1 10 0 1 0 ] , B = [ 0 − 1 1 1 − 1 3 5 0 ] , C = [ 1 − 1 1 1 1 1 1 1 ] .Evaluate: A B

To determine

To calculate: The value of AB when A=[010110010], B=[01111350] and C=[11111111].

Explanation

Given Information:

The provided values is:

A=[0âˆ’10110010], B=[0âˆ’111âˆ’1350] and C=[1âˆ’1111111]

Formula Used:

Multiplication of Matrices:

If A is an mÃ—n matrix and B is an nÃ—k matrix, then the product AB is the mÃ—k matrix whose ijth entry is the product

(AB)ij=[ai1ai2ali3...ain][b1jb2jb3j...bnj]=ai1b1j+ai2b2j+ai3b3j+...+ainbnj

Calculation:

Consider the provided values:

A=[0âˆ’10110010], B=[0âˆ’111âˆ’1350] and C=[1âˆ’1111111]

For calculating the value of AB, substitute their given respective values as:

AB=[0âˆ’10110010][0âˆ’111âˆ’1350]

Here, A=[0âˆ’10110010] and B=[0âˆ’111âˆ’1350].

First, check whether the dimensions of A and B match up.

Dimensions of A=2Ã—4 and dimensions of B=4Ã—2. So, the second term and the first term in the dimensions of A and B respectively, are same, i.e. 4.

Hence, the dimensions of the matrices match up and the product of these two matrices is defined and will be of the order 2Ã—2.

As, multiplication of Matrices is given by:

If A is an mÃ—n matrix and B is an nÃ—k matrix, then the product AB is the mÃ—k matrix whose ijth entry is the product

(AB)ij=[ai1ai2ali3...ain][b1jb2jb3j...bnj]=ai1b1j+ai2b2j+ai3b3j+

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