   Chapter 4.2, Problem 31E

Chapter
Section
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=, B= and C=.

Explanation

Given Information:

The provided values is:

A=, B= and C=

Formula Used:

Multiplication of Matrices:

If A is an m×n matrix and B is an n×k matrix, then the product AB is the m×k matrix whose ijth entry is the product

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

Calculation:

Consider the provided values:

A=, B= and C=

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

AB=

Here, A= and B=.

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

Dimensions of A=2×4 and dimensions of B=4×2. 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 2×2.

As, multiplication of Matrices is given by:

If A is an m×n matrix and B is an n×k matrix, then the product AB is the m×k matrix whose ijth entry is the product

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

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