Elementary Operations of a Matrix

  

The following three operations applied on the rows (columns) of a matrix are called elementary row (column) transformations.

(i) Interchange of any two rows (columns)

If ith row (column) of a matrix is interchanged with the jth row (column), it will be denoted by Ri ↔ Rj (Ci ↔ Cj).

For example: A = matrix22, then by applying R1 → R2 we get B = matrix23.

(ii) Multiplying all elements of a row (column) of a matrix by a non-zero scalar. If the elements of ith row (column) are multiplied by non-zero scalar k, it will be denoted by Rl→Ri (k) [Ci→Ci (k)] or Rl→kRi [Ci→kCi].

       If A = matrix24, then by applying R2 → 3R2, we obtain B = matrix25.

(iii) Adding to the elements of a row (column), the corresponding elements of any other row (column) multiplied by any scalar k.

       If k times the elements of jth row (column) are added to the corresponding elements of the ith row (column), it will be denoted by Ri→Ri + k Rj (Ci→Ci + kCj).

       If A=matrix26, then application of elementary operation R3→R3 + 2R1 lead to B =matrix27.

 

Illustration:

  Using elementary row transformations and find the inverse of the matrix A= matrix28.

Solution:

 matrix29
       

matrix30

IIT JEE and AIEEE study material is available online free of cost at askIITians.com. We offer numerous live online courses, online tests and other interesting sections as well for IIT JEE and AIEEE preparation - you do not need to travel anywhere any longer - just sit at your home and study for IIT JEE and AIEEE live online with askIITians.com
 

  

  

Name
Email Id
Mobile

Exam
Target Year

Related Resources
Operations on Determinants

Operations on Determinants Multiplication of two...

Minors and Co-Factors

Minors and Co-Factors The minor of an element of a...

System of Linear Equations

System of Linear Equations System of Linear...

Algebra of Matrices

Algebra of Matrices Addition and Subtraction of...

Determinants Definitions Properties

Determinants Definitions & Properties...

Solved Examples Part-1

IIT JEE Download IIT JEE Solved Examples on...

Matrices

Matrices: Definition and Classification DEFINITION...

System of Simultaneous Linear Equations

System of Simultaneous Linear Equations System of...

Special Matrices

Special Matrices Symmetric and Skew Matrices A...