The document provides an introduction to matrices, including: - Matrices are rectangular arrays of elements displayed in rows and columns. They can represent transformations, systems of equations, and more. - The order or size of a matrix is the number of rows and columns. For example, an m x n matrix has m rows and n columns. - Common types of matrices include row matrices, column matrices, square matrices, diagonal matrices, symmetric matrices, and more. - Basic matrix operations include addition, subtraction, and multiplication. Properties like commutativity and distributivity apply. - Matrices have applications in fields like biology, chemistry, and more. They can model structures like extracellular matrices and crystal structures.

1. WELCOME

2. A. DALLY MARIA EVANGELINE
ASSISTANT PROFESSOR
PG & RESEARCH DEPARTMENT OF
MATHEMATICS
BON SECOURS COLLEGE FOR WOMEN
THANJAVUR
MATRICES

3.  The term ‘matrix’ was first introduced by Sylvester in 1850. He
defined a matrix to be an arrangement of terms.
 Knowledge of matrix is very useful and important as it has a
wider application in almost every field of mathematics.
 The purpose of matrices is to provide a kind of mathematical
shorthand to help the study of problems represented by the
entries.
 The matrices may represent transformations of co-ordinate
spaces or systems of simultaneous linear equations.
INTRODUCTION

4. This representation gives the
following informations.
 The elements along the rows
represent the height, weight,
age and pulse rate of the each
patient.
 The elements along the first,
second, third, fourth and fifth
columns represent the height,
weight, age and pulse rate of
the patients.
SIMPLE EXAMPLE

5.  A matrix is a rectangular array or arrangement of
entries or elements displayed in rows and columns
put within a [] and ().
 The entries or elements may be any kind of numbers
(real or complex), polynomials or other expressions.
DEFINITION OF A MATRIX

6.  The order or size of a matrix is the number of rows and
the number of columns that are present in a matrix.
 Example of an m × n matrix
ORDER OR SIZE OF A MATRIX

7. TYPES OF MATRICES

8. ROW AND COLUMN MATRICES
 A matrix having only one
row - row matrix.
 Example:
 A = [1 -7 4]
 B = [22]
 C = [5 8 9 6]
 A matrix having only one
column – column matrix
 Examples:
 A =
1
9
6

9. SQUARE AND DIAGONAL MATRICES
 Matrix having equal
number of rows and
columns
 Order = n × n. Also called
square matrix of order n
 Number of elements in a
square matrix of order n
is 𝑛2
 Matrix having elements
along the main diagonal
 Other entries are zero

10.  SYMMETRIC MATRIX 𝑎𝑖𝑗 = 𝑎𝑗𝑖
 𝐴 𝑇 = 𝐴
SOME PROPERTIES OF SQUARE
MATRIX

11.  Let A be any square matrix. Then 𝐴 𝑇 + 𝐴 is symmetric
 A + B
 AB is symmetric iff AB = BA
 AB + BA is symmetric
 If A is symmetric, then kA is symmetric where k ЄF
PROPERTIES OF SQUARE MATRICES

12.  Addition and Subtraction
 Matrix multiplication
 Row-switching (swapping the rows)
OPERATIONS OF MATRICES

13.  Matrix addition is commutative A+B = B+A
 Matrix addition is associative A(B+C) = (A+B) +C
 Additive identity A + O = O + A = A
 Additive inverse A + (-A) = (-A) + A = O
 Matrix multiplication is not commutative
 Matrix multiplication is associative
 Matrix multiplication is distributive
ALGEBRAIC PROPERTIES OF
MATRICES

14. REAL LIFE APPLICATION OF
MATRICES

17. MATRIX IN BIOLOGY
EXTRACELLULAR MATRIX
A meshwork
of proteins and carbohydrates
that binds cells together or
divides one tissue from another.

19. MATRIX IN CHEMISTRY
CRYSTAL DOT
MODEL

21. 1. Use the matrix built-in
function to create a data
set based on the above
function.
2. Plot the matrix and
change the Surface Fill and
the Trace Color.
Plotting a Matrix Created from a
Function