2. Order of a matrix

A matrix is represented in the form \((\text{Number of rows})\) \(\times\) \((\text{Number of column})\).

 

Let us consider a matrix with the '\(m\)', the number of rows and '\(n\)', the number of columns.

 

Then the matrix is represented as \(m\) \(\times\) \(n\).

 

\(m\) \(\times\) \(n\) can be either be read as \(m\) 'cross' \(n\) or \(m\) 'by' \(n\).

 

The general form of a \(m\) \(\times\) \(n\) matrix is given by:

 

 

Here, \(a_{11}\), \(a_{12}\), and so on are entries of a matrix.

 

The general form of an entry of a matrix is \(a_{ij}\), where '\(i\)' represents the \(i^{th}\) row of the matrix and '\(j\)' represents the \(j^{th}\) column of the matrix. An entry of a matrix can also be represented as the \((i\), \(j)^{th}\) element.

 

A matrix '\(A\)' can also be represented as \(A\) \(=\) \((a_{ij})_{m \times n}\) where \(i\) \(=\) \(1\), \(2\), \(3\)\(...m\) and \(j\) \(=\) \(1\), \(2\), \(3...n\).

 

The total number of elements in the matrix \(A\) \(=\) \((a_{ij})_{m \times n}\) is given by \(mn\).