Matrix Introduction





In this page matrix introduction,we are going to see definition of matrix and their types.

Definition:

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 ...... a1n
a21 a22 ...... a2n
: : : :
ai1 ai2 .... ain
: : : :
am1 am2 ...... amn
 

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 the first row and first column = 5

The element which occurs in the first row and second column = -2

The element which occurs in the first row and third column = 7

The element which occurs in the first row and fourth column = 9

The element which occurs in the second row and first column = 3

The element which occurs in the second row and second column = 1

The element which occurs in the second row and third column = 2

The element which occurs in the second row and fourth column = -8atrix introduction

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 aij is the determinant obtained by deleting the ith row and jth column in which the element aij stands. The minor of aij by Mij.

Cofactor of matrix

The cofactor is a signed minor. The cofactor of aij is denoted by Aij and is defined as Aij = (-1) ^(i+j) Mij.

 
+ - +
- + -
+ - +
 

Adjoint of matrix

Let A = [aij] be a square matrix of order n. Let Aij be a cofactor of aij. Then nth order matrix [Aij]^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.

Inverse of matrix

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

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