Concept of Matrices

Now, we write formal definition of Matrix.
An arrangement of number into m-rows and n-columns is called a Matrix of order m{\text{x}}n.
Matrix always denoted by capital letters A,B,C, \ldots whereas their elements or entries by small letters a,b,c, \ldots

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 matrix in tabular form, matrix 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

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