Determine The Order Of Matrix - Practice Questions & MCQ

A rectangular arrangement of objects (numbers or symbols or any other objects) is called a matrix (plural: matrices).

Example:

1.         
2.         
3.         

 

Order of Matrix

Rows and Columns:

The horizontal objects denote a row and vertical ones denote a column.

Eg, in first matrix above, elements 2, 4 and -3 lie in first row and 5, 4 and 6 in second row

Also 2, 5, lie in first column, 4,4 in second column, and -3, 6 in third column

 

Order of a matrix: 

Matrix of order m × n, (read as m by n matrix) means that the matrix has m number of rows and n number of columns.

E.g.,

• First matrix has order 2 x 3
• Second matrix has order 3 x 2
• Third matrix has order 4 x 1

 

Representation of a m x n matrix:

This representation can be represented in a more compact form as  

Where  represents element of i^th row and j^th column and i = 1,2,...,m; j = 1,2,...,n.

 

For example, to locate the entry in matrix A identified as a_ij, we look for the entry in row i, column j. In matrix A, shown below, the entry in row 2, column 3 is a₂₃.

Note:

Matrix is only a representation of the symbol, number or object. It does not have any value. Usually, a matrix is denoted by capital letters.

 

Types of Matrices

Row matrix: A matrix containing only one row is called a row matrix. So a matrix   is said to be a row matrix when m = 1.

It can be denoted by

 

Eg, 

[ 1    32    81    -32 ] has only 1 row. It has order 1 x 4

 

Column matrix: A matrix containing only one column is known as a column matrix. So a matrix    is said to be column matrix when n = 1.

It is denoted by

Eg,

This matrix has order 4 x 1

 

Note:

A matrix that contains only one row or one column is also known as a vector i.e. row vectors and column vectors.