   Chapter 10.2, Problem 12ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# Let O denote the matrix [ 0 0 0 0 ] . Find 2 × 2 matrices A and B such that A ≠ O and B ≠ O but A B = O .

To determine

Find 2 × 2 matrices A and B such that AO and BO, but AB = O.

Explanation

Given information:

Let O denote the matrix .

Calculation:

We have O=

For example, let us choose the following two 2 x 2-matrices:

A=[ 1 0 1 0]OB=[ 0 0 1 1]O

The first matrix has dimensions 2 × 2 and the second matrix has dimension 2 × 2. Since the inner dimensions are equal, we can multiply the matrices. Moreover, the product should be a 2 × 2-matrix.

Multiply the rows of the first matrix with the columns of the second matrix (adding the products of the corresponding elements):

AB=[ 1 0 1 0][ 0 0 1 1]<

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