Summary COMPUTATIONAL MATHEMATICS ( MMEC511 ) ( MCMT511 ) - SOL PLAATJE MATRIX LECTURE NOTES

(Section 8.1: Matrices and Determinants) 8.01

CHAPTER 8: MATRICES and DETERMINANTS

The material in this chapter will be covered in your Linear Algebra class (Math 254 at Mesa).


SECTION 8.1: MATRICES and SYSTEMS OF EQUATIONS

PART A: MATRICES

A matrix is basically an organized box (or “array”) of numbers (or other expressions).
In this chapter, we will typically assume that our matrices contain only numbers.


Example

Here is a matrix of size 2
3 (“2 by 3”), because it has 2 rows and 3 columns:


1 0 2 
 
0 1 5 

The matrix consists of 6 entries or elements.


In general, an m
n matrix has m rows and n columns and has mn entries.


Example

Here is a matrix of size 2
2 (an order 2 square matrix):

 4
1
 
3 2 

The boldfaced entries lie on the main diagonal of the matrix.
(The other diagonal is the skew diagonal.)

, (Section 8.1: Matrices and Determinants) 8.02

PART B: THE AUGMENTED MATRIX FOR A SYSTEM OF LINEAR EQUATIONS

Example

3x + 2 y + z = 0
Write the augmented matrix for the system: 

2x
z = 3

Solution

Preliminaries:

Make sure that the equations are in (what we refer to now as)
standard form, meaning that …

• All of the variable terms are on the left side (with x, y, and z
ordered alphabetically), and

• There is only one constant term, and it is on the right side.

Line up like terms vertically.

Here, we will rewrite the system as follows:

 3x + 2 y + z = 0


2x
z=3

(Optional) Insert “1”s and “0”s to clarify coefficients.

 3x + 2 y + 1z = 0


2x + 0 y
1z = 3

Warning: Although this step is not necessary, people often
mistake the coefficients on the z terms for “0”s.