Order Of Matrices

The arrangement of elements as number of rows and columns in a matrix is known as order of matrix. It represents the number of rows and columns present in the matrix. It simply tells us about the dimension of the matrix. From the order of the matrix, we can find the number of elements present in the matrix. It is represented by m x n.

Example:

 In the above matrix, the number of rows is equal to 2 and the number of columns is also equal to 2. Therefore, the order of the matrix, m x n = 2 x 2 

To Find The Number of Elements in The Matrix 

The number of elements in any matrix can simply be obtained by multiplying the number of rows and columns present in the matrix. In other words, we can find the elements from the order of the matrix.

Example: 

 The number of elements in the given matrix is 3 x 2 = 6.

Classification Of Matrices based on Their Order

Matrices can be classified based on their order. Dimension of the matrix helps us to identify the type of the matrix. Let us see the type of matrices based on their order.

• Row matrix – In this type of a matrix, the number of rows is always one. However, the number of columns can be greater than 1. It is represented by 1 x n. where n represents the number of columns.
• Column Matrix – In this type of matrix, the number of columns is equal to one. It is represented by m x 1. Where M represents the number of rows.

Zero Matrix – This matrix is also called null matrix or void matrix. Zero Matrix can have any number of rows and columns. But each element of the zero matrix is 0, which is why it is known as null matrix or void matrix.

• Square Matrix – In a square matrix, the number of rows and the number of columns is always the same. Its order can be represented as m x m.
• Rectangular Matrix – When the number of rows and columns in the matrix is different, then the matrix is known as rectangular matrix. The order of the rectangular matrix is of the order m x n.
  

  Conclusion 

  A matrix is a 2-dimensional rectangular array of numbers or functions. Each entity in the matrix represents the element of the matrix. The dimension of the matrix is the size of the matrix, which is also known as the order of the matrix. The order of the matrix represents the number of rows and columns present in the matrix. It is represented by ‘m x n ‘. The number of horizontal lines present in each array of a matrix are known as rows of the matrix, and the number of vertical lines is known as columns. The number of elements in the matrix can be found by multiplying the number of rows and columns of the matrix. Matrices can be classified based on their order. Dimension of the matrix helps us to identify the type of the matrix. Based on the order of the matrix, the matrix is classified as row matrix, column matrix, null matrix, zero matrix, square matrix, and rectangular matrix.