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.