Order of a Matrix

A system of expressing the number of rows and numbers of columns of a matrix in mathematical form is defined the order of the matrix.

The order of a matrix denotes the arrangement of elements as number of rows and columns in a matrix. So, it is known as dimension of a matrix. It is usually expressed as the number of rows is multiplied by the number of columns in mathematics but it is read as number of rows by number of columns.

One important factor is, the dimension of the matrix tells the number of elements of the matrix. It can be obtained by multiplying the rows by columns.

Consider a matrix $M$ and its elements are displayed in matrix form as follows.

$M=\left[\begin{array}{ccc}5& 8& 1\\ \u20134& 6& 9\end{array}\right]$

The elements $5,8$ and $1$ are displayed in one row and the elements $\u20134,6$ and $9$ are displayed in another row. Every three elements are displayed in a row in this matrix. Therefore, the total number of rows used to form this matrix is $2$.

The elements $5$ and $\u20134$ are displayed in one column. $8$ and $6$ are displayed in another column. $1$ and $9$ are displayed in another column. Every two elements are displayed in a column. Therefore, the total number of columns used to form this matrix is $3$.

The number of rows multiplied by the number of columns is called as order of the matrix. For this reason, $2\times 3$ is order of the matrix. It is read as $2$ by $3$ matrix.

The order of the matrix is usually written as subscript to matrix.

$M={\left[\begin{array}{ccc}5& 8& 1\\ \u20134& 6& 9\end{array}\right]}_{2\times 3}$

The order of the matrix is also useful to know the number of the elements of the matrix. In order to know the number of elements of the matrix, calculate the product of the order of the matrix.

The total number of elements $=2\times 3=6$

Now, count all the elements of this matrix and they are $6$. The product of the order of the matrix is equal to the total number of elements of the matrix.

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