Matrix Introduction

MATRIX INTRODUCTION

A matrix is a rectangular array or arrangement of entries or elements displayed in rows and columns within a square bracket [ ] or parenthesis ( ).

Usually matrices are denoted by the capital letters like

A, B, C .....

1	2	3	4
5	6	7	8

A	B
C	D
1	2
3	4

In any matrix

Horizontal arrangements are known as rows
The vertical arrangements are known as columns

-1	0	3

5	2	-1

First row

Second row

Order of a matrix :

A matrix having m rows and n columns is called matrix of order m x n or simply m x n matrix . In general m x n has the following form

a₁₁	a₁₂	......	a_1n
a₂₁	a₂₂	......	a_2n
:	:	:	:
a_i1	a_i2	....	a_in
:	:	:	:
a_m1	a_m2	......	a_mn

The order of a matrix or the size of a matrix is known as the number of rows or the number of columns which are present in that matrix.

5	-2	7	9
-3	1	2	-8

The order of above matrix is 2 x 4. Because in the above matrix there are two rows and four columns.

The element which occurs in a₁₁ = 5

The element which occurs in a₁₂= -2

The element which occurs in a₁₃ = 7

The element which occurs in a₁₄= 9

The element which occurs in a₂₁= 3

The element which occurs in a₂₂ = 1

The element which occurs in a₂₃ = 2

The element which occurs in a₂₄ = -8

Minor of matrix :

Minor of a matrix may defined as follows.

Let |A| = |[a_ij]| be a determinant of order n.

The minor of an arbitrary element a_ij is the determinant obtained by deleting the i^th row and j^th column in which the element a_ij stands. The minor of a_ij by M_ij.

Examples of finding minor of a matrix

Cofactor of matrix :

The cofactor is a signed minor. The cofactor of a_ij is denoted by A_ij and is defined as A_ij = -1^(i+j) M_ij.

+	-	+
-	+	-
+	-	+

Examples of finding cofactor of matrix

Adjoint of matrix :

Let A = [a_ij] be a square matrix of order n. Let A_ij be a cofactor of a_ij. Then nth order matrix [A_ij]^T is called adjoint of A. It is denoted by adj A. In other words we can define adjoint of matrix as transpose of co factor matrix.

Examples of finding adjoint of matrix

Inverse of matrix :

If A is a non-singular matrix,there exists an inverse which is given by

Examples of finding inverse of matrix

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MATRIX INTRODUCTION

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