Matrices and Determinants

K.KUMARAVELU, Dec 29, 2021

This book is about matrices and determinants.

Table of Contents

  1. Matrices
    1. Introduction
  2. Order or Size of the matrix
    1. Definition
  3. Types of Matrices
    1. Row, Column, Zero Matrices
    2. Square, Diagonal, Unit, Triangular Matrices
    3. Scalar matrix
  4. Types of Matrices -Presentation
    1. Power Point Presentation
  5. Algebraic Operations on Matrices
    1. Activity-1
    2. Activity-2
  6. Determinants
    1. Activity - Determinants
  7. Assessment
    1. Quiz -Choose the correct answer

1.

Matrices

  • 1. Introduction

1.1.

Introduction

Matrices
A matrix is a rectangular array or arrangement of entries or elements displayed in rows and columns put within a square bracket [ ].
Matrices are denoted by capital letters [math]A,B,C,...[/math] etc.
General form of a matrix
If a matrix[math]A[/math] has [math]m[/math] rows and [math]n[/math] columns, then it is written as [br][math]A=\left[a_{ij}_{ }\right]_{m\times n},1\le i\le m,1\le j\le n.[/math]
Example of matrices
In a matrix, the horizontal lines of elements are known as rows and the vertical lines of elements are known as columns.
Above matrix [math]A[/math] has [math]2[/math] rows and [math]2[/math] columns, [math]B[/math] has [math]3[/math] rows and [math]3[/math] columns.
– K.KUMARAVELU

2.

Order or Size of the matrix

  • 1. Definition

2.1.

Definition

If a matrix [math]A[/math] has [math]m[/math] rows and [math]n[/math] columns then the[b] order or size [/b]of the matrix [math]A[/math] is defined to be [math]m\times n[/math] ( read as [math]m[/math] by [math]n[/math] ).
The order or size of the matrix [math]A[/math] is
The order or size of the matrix [math]B[/math] is
– K.KUMARAVELU

3.

Types of Matrices

  • 1. Row, Column, Zero Matrices
  • 2. Square, Diagonal, Unit, Triangular Matrices
  • 3. Scalar matrix

3.1.

Row, Column, Zero Matrices

Row matrix
A matrix having only one row is called a[b] row matrix[/b]
row matrix of order [math]1\times4[/math].
Column matrix
A matrix having only one column is called a [b]column matrix.[/b]
column matrix of order [math]4\times1[/math].
Zero matrix or Null matrix or Void matrix
A matrix [math]A=\left[a_{ij}\right]_{m\times n}[/math] is said to be a[b] zero matrix or null matrix or void matrix[/b] denoted by [math]O[/math] if [math]a_{ij}[/math] for all values of [math]1\le i\le m[/math] and [math]1\le j\le n.[/math]
zero matrices of order [math]2\times4[/math]
– K.KUMARAVELU

3.2.

–

3.3.

–

4.

Types of Matrices -Presentation

  • 1. Power Point Presentation

4.1.

Power Point Presentation

TYPES OF MATRICES
– K.KUMARAVELU

5.

Algebraic Operations on Matrices

  • 1. Activity-1
  • 2. Activity-2

5.1.

Activity-1

1. multiplication of a matrix by a scalar[br]2. addition and subtraction of two matrices and [br]3. multiplication of two matrices
– K.KUMARAVELU

5.2.

–

6.

Determinants

  • 1. Activity - Determinants

6.1.

Activity - Determinants

To every square matrix [math]A=\left[a_{ij}\right][/math] of order [math]n\times n[/math], we can associate a number called the [b]determinant [/b]of the matrix [math]A[/math]
Determinant can be defined only for square matrices.
Determinant of matrix of order 2 by 2.
– K.KUMARAVELU

7.

Assessment

  • 1. Quiz -Choose the correct answer

7.1.

Quiz -Choose the correct answer

1.The transpose of a rectangular matrix is a[br]
2.The transpose of a row matrix is a[br][br]
3.The transpose of a column matrix is a[br][br]
4.A matrix [math]A[/math] is said to be conformable for multiplication with a matrix [math]B[/math] if[br][br]
5.if [math]det\left(A\right)=0[/math], then [math]A[/math] is called a
6.if, [math]det\left(A\right)\ne0[/math], then [math]A[/math] is called a
7. A matrix having [math]m[/math] rows and [math]n[/math] columns with [math]m\ne n[/math] is said to be a
– K.KUMARAVELU

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