Solved Examples on Order of Matrix
Example 1: Determine the order of the matrix given below.
Solution:
Number of rows in the given matrix A = 5
Number of columns in the given matrix A = 4
We know that the order of the matrix = number of rows Γ number of columns
Therefore, the order of the given matrix A = 5 Γ 4
Example 2: If βPβ is a matrix of order β2 Γ 3β and βQβ is a matrix of order β3 Γ 3β, then what is the order of the matrix βP + Qβ?
Solution:
Given data:
The order of the matrix βPβ = β2 Γ 3β
The order of the matrix βQβ = β3 Γ 3β
We can see that the order of the given matrices is different. So, the βP + Qβ matrix does not exist, as we cannot add two matrices of different orders.
Example 3: Determine the order of the matrix, if a matrix βBβ has ten elements in total.
Solution:
Given data:
Number of elements in matrix B = 10
Now, write all the possible factors of 10.
10 = 1 Γ 10
10 = 2 Γ 5
10 = 5 Γ 2
10 = 10 Γ 1
Hence, we have four different ways to write the order of a matrix βBβ, for the given number of elements they are A1Γ10, A2Γ5, A5Γ2, A10Γ1
Example 4: Determine the types of matrices based on the order of the matrices.
- A2Γ3
- B1Γ5
- C4Γ4
- D2Γ1
Solution:
- A2Γ3 The given matrix βAβ has two rows and three columns. So, βAβ is a rectangular matrix as the number of rows in the matrix is not equal to the number of columns.
- B1Γ5 The given matrix βBβ has one row and five columns. So, βBβ is a row matrix as it has one row and five columns.
- C4Γ4 The given matrix βCβ has four rows and four columns. So, βAβ is a square matrix as the number of rows in the matrix is equal to the number of columns.
- D2Γ1 The given matrix βDβ has one column and two rows. So, βDβ is a column matrix as it has one column and two rows.
Order of Matrix
Order of the matrix defines the number of rows and columns that a matrix has. In a matrix, data is arranged as an array of elements. This data is arranged in rows and columns, and the number of rows and columns any matrix has defines the Order of the matrix. Suppose any matrix has 5 rows and 3 columns then the order of the matrix is 5Γ3.
In this article, we will learn about the order of matrices in detail.
Table of Content
- What is Order of Matrix?
- How to Determine the Order of Matrix?
- Type of Matrices Based on Order of Matrix
- Important Points on Order of Matrix
- Solved Examples
- FAQs