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A useful way to test new ideas in matrix algebra, or to make conjectures, is to make calculations with matrices selected at random. Checking a property for a few matrices does not prove that the property holds in general, but it makes the property more believable. Also, if the property is actually false, you may discover this when you make a few calculations.[M] Write the command(s) that will create a $6 \times 4$ matrix with random entries. In what range of numbers do the entries lie? Tell how to create a $3 \times 3$ matrix with random integer entries between $-9$ and $9 .[\text { Hint: If } x \text { is a random number }$ such that $0 < x < 1$ , then $-9.5 < 19(x-.5) < 9.5 . ]$

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Algebra

Chapter 2

Matrix Algebra

Section 1

Matrix Operations

Introduction to Matrices

McMaster University

Harvey Mudd College

Lectures

01:32

In mathematics, the absolu…

01:11

03:05

A useful way to test new i…

03:30

01:39

[M] Construct a random $4 …

01:24

For a randomly generated $…

01:08

Show that for$$A=\left…

01:58

PROPERTIES OF DETERMINANTS…

02:40

02:21

CONJECTURE A $\textbf{tria…

10:38

Verify property P9 for the…

01:40

Conjecture Consider square…

for this problem, we need to figure out how to generate a random matrix of a given size. Now, the answer to this problem is totally dependent upon which, uh, software application you are using. Um, every single one is different. So you really need to research your particular one. Um, for me, I like to use the desk. Most application to do my online. It's got a graphing calculator in a matrix calculator. One thing it does not do well, though, is to do random matrices. So for me, if I'm going to great generate a random matrix, I'm going to go to Google Sheets. This is a free application. It's it's out like Microsoft Excel. Um, it's a spreadsheet, and the tool that I use is the rand between and you can see I've got that highlighted here. So the tool for me I type in rand between. So that is a random number, and I could tell I could tell it what numbers I wanted to be between. I could have between one and 10 between zero and 100. In this particular case, we wanna have numbers between negative nine and nine. So this is the command that I'll put into the box. As you can see in this case, when I did ran between, it gave me a negative three. So if I wanted to make ah three by three Matrix, I could just drag that. So now every square is rand between, but you can see that I have different values. If I wanted this to be a bigger matrix, I could do it to be, Let's see, before five. I could do with six by a four. Okay, so whatever size I need And if I needed it again, I could I could keep doing this. Every time I selected this, it would give me different values for this. And so then I can use these as inputs to him into a matrix in death most or any other matrix calculator software. So again, this is one way to do it. And it's certainly not the only way. Every software does have specific things, So please research what you use to see how to do this best

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