Concept of Matrices

Matrix:

Now we will write formal definition of a matrix.

An arrangement of numbers into m-rows and n-columns is called a matrix of order m{\text{x}}n.

A matrix always denoted by capital letters A,B,C, \ldots whereas their elements or entries are denoted by small letters a,b,c, \ldots
e.g.

A = \left[ {\begin{array}{*{20}{c}} {{a_{11}}}&{{a_{12}}}&{{a_{13}}}&{...}&{{a_{1n}}} \\ {{a_{21}}}&{{a_{22}}}&{{a_{23}}}&{...}&{{a_{2n}}} \\ .&.&.&{...}&. \\ {{a_{m1}}}&{{a_{m2}}}&{{a_{m3}}}&{...}&{{a_{mn}}} \end{array}} \right]

This form of matrix is called a matrix in tabular form. Matrices can also be written in short form or abbreviated form as:

A = \left[ {{a_{ij}}} \right],{\text{ }}i = 1,2,3,...,m{\text{ }}j = 1,2,3,...,n

The Order of a Matrix:
The number of rows and the number of columns in a matrix is called the order of the matrix, denoted by m{\text{x}}n or (m,n), where m = number of rows, n = number of columns.