## Introduction of Matrices

**Introduction of Matrices:**

A rectangular array of number is called a matrix. Each number is called the element or entry of the matrix. A Row of a matrix is a horizontal array and a column is a vertical one. The size or order of a matrix is determined by the number of rows and column of that matrix. A matrix is said to be of order or size m n if it has m rows and n column. If m = n, the matrix is called the square matrix of order or size n n. Any real number is called a scalar.

There are a number of ways to represent an m n matrix.

Where a_{ij} with i = 1,2..... m; j = 1,2....n are called the elements of the matrix.

**Example-1:
**

is called a Square matrix of size n n or simply n.

The element a_{ij }where i = j from main **diagonal** of the matrix. So the matrix

Such amatrix is called a** Column** Vector as for a 1 n matrix is called a **row** vector.

**Example-2:** Consider a matrix;

The diagonal element are denoted by δ; The super diagonal element are denoted by α; and the sub diagonal is denoted by β.