CHAPTER 2
MATRICES
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Introduction
Types of Matrices
Operations
INTRODUCTION
Definition 2.1
A matrix is a rectangular array of elements or entries
aij involving m rows and n columns
Columns, n
 a11
a
 21
A   a31

 
 ai1

a12
a13

a22
a23

a32
a33




ai 2
ai 3

a1 j 
Rows, m
a2 j 
a3 j   amn mn

 
aij 
INTRODUCTION
Definition 2.2
i. 2 matrices A  aij  M mn and B  bij   M rs
 
are said to be equal iff m = r and n = s then A =
B.
ii. If aij for i = j, then the entries a11,a22,a33,… are
called the diagonal of matrix A
 
INTRODUCTION
Example 2.1
Find the values for the variables so that the matrices
in each exercise are equal.
 x  1 y  2  10  5

 2z


8   6 8 

TYPES OF MATRICES
Square Matrix
Matrix with order n x n
1 2
A

3 4 22
1 2 3
B  4 5 6
7 8 9 33
TYPES OF MATRICES
Diagonal Matrix
TYPES OF MATRICES
Scalar Matrix
TYPES OF MATRICES
Identity Matrix
TYPES OF MATRICES
Zero Matrix
TYPES OF MATRICES
Negative Matrix
TYPES OF MATRICES
Upper-triangular & Lower-triangular
Matrix
TYPES OF MATRICES
Upper-triangular & Lower-triangular
Matrix
TYPES OF MATRICES
Matrix Transpose
TYPES OF MATRICES
Matrix Transpose
TYPES OF MATRICES
Symmetric Matrix
TYPES OF MATRICES
Skew-Symmetric Matrix
TYPES OF MATRICES
Row Echelon Form (REF)
TYPES OF MATRICES
Reduced Row Echelon Form (RREF)
Addition of Matrices
Substraction of Matrices
Addition & Substraction of Matrices
Scalar Multiplication of Matrices
Matrix Multiplication