Definition of a Matrix

Consider the arrangement

In this arrangement, there are two rows and four columns. The number 3 lies in the 2^nd row and 4^th column. Each number has a fixed position.

Matrix A has 2 rows and 3 columns and is thus of order 2 x 3. Matrix B has 3 rows and 2 columns and is thus of order 3 x 2. The plural for "matrix" is "matrices". Capital letters are used to denote matrices.

Definition of a Matrix

A rectangular array of entries is called a Matrix. The entries may be real, complex or functions.

The entries are also called as the elements of the matrix.

The rectangular array of entries are enclosed in an ordinary bracket or in square bracket. Matrices are denoted by capital letters.

Example:

(i)

Note that the entries in a given matrix need not be distinct.

(ii)

The entries in this matrix are function of x.

A matrix having m rows and n columns is called as matrix of order mxn. Such a matrix has mn elements.

In general, an mxn matrix is in the form

Where a_ij represents the element in i^th column.

The above matrix may be denoted as A = [a_ij]_mxn.