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 $mn$.