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 ...... 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 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|  =  |[aij]| 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.

Examples of finding minor of a matrix

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.

 + - + - + - + - +

Examples of finding cofactor 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.

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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