in properties of determinants how do we apply c1-c1+c2+c3 or ri-r1+r2+r3 in any row or column plz xplain wid an example

First of all make it clear in your mind that what elementary transformations you can apply to find the inverse of matrix.

The elementary transformations that can be applied to a matrix are:

1. Interchange of any two rows or columns of a matrix

 It is denoted as Ri ↔ Rj or Ci ↔ Cj


2. Elements of any row or column multiplied by a non-zero number

 It can be denoted as RikRi of CikCi,where k is a non-zero constant.


3. Addition to the elements of any row or column; the corresponding elements of any other row 

or column multiplied by any non-zero number.

It is denoted as Ri → Ri + kRj or Ci → Ci + kCj.


Using these operations we can find the inverse of a given matrix. The steps of algorithm to find the inverse of given matrix are:



Step 1. Obtain the square matrix, say A

Step 2. Write A = In A

Step 3. Perform the sequence of elementary operations on A on the LHS and the pre-factor In on the RHS till we obtain the result In = BA

Step 4. Write A-1 = B


Here is an example to find the inverse of the given matrix, using the elementary row operations:

Find the inverse of the matrix.



Now, A = IA


After getting this concept,you are suggested to go through the study material again. This 

concept is explained nicely with the help of video in our study material.That will help you a lot.

Still if you face any problem, then do get back to us.

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c1 -- c1 +c2+c3 means we have to add elements of  column 1 , column 2 , column3   and write the result in  place of column 1

  • 3

 means we add first elements of c1 c2 n c3 n write the reslt in c1

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