NCERT Solutions Class 12

NCERT Solutions Class 12

Matrices : NCERT Solutions – Class 12 Maths (Ex 4)

Exercise 3.4

Using elementary transformation, find the inverse of each of the matrices, if it exists in Exercises 1 to 6.

1.  

Ans. Let A = 

Since A = IA     

    

    

    

   = 


2.    

Ans. Let A = 

Since A = IA     

     

     

    

   = 


3.  

Ans. Let A = 

Since A = IA     

      

     

    

   = 


4.      

Ans. Let A = 

Since A = IA     

      

     

    

    

   = 


5.    

Ans. Let A = 

Since A = IA     

      

     

     

   = 


6.  

Ans. Let A = 

Since A = IA     

      

     

      

     

   = 


 

Using elementary transformation, find the inverse of each of the matrices, if it exists in Exercises 7 to 14.

7.    

Ans. Let A = 

Since A = IA     

      

     

     

     

   = 


8.   

Ans. Let A = 

Since A = IA     

      

     

     

   = 


9.   

Ans. Let A = 

Since A = IA     

      

     

     

   = 


10.  

Ans. Let A = 

Since A = IA     

      

     

     

     

     

   = 


11.   

Ans. Let A = 

Since A = IA     

     

     

     

     

   = 


12.   

Ans. Let A = 

Since A = IA     

     

     

Here, all entries in second row of left side are zero.

   does not exist.


13. 

Ans. Let A = 

Since A = IA     

     

      

      

   = 


14.  

Ans. Let A = 

Since A = IA     

     

     

Here, all entries in second row of left side are zero.

   does not exist.


 

Using elementary transformation, find the inverse of each of the matrices, if it exists in Exercises 7 to 14.

15.     

Ans. Let A = , We know that A = IA,    

    

    

    

    

    

    

   

    

  


16.    

Ans. Let A = , Since, A = IA     

    

    

    

    

    

    

   = 


17.  

Ans. Let A = , Since, A = IA     

    

    

    

    

    

    

   = 


 

18.  Matrices A and B will be inverse of each other only if:

(A) AB = BA 

(B) AB = BA = 0

(C) AB = 0, BA = I

(D) AB = BA = I

Ans. By definition of inverse of square matrix,

Option (A) is correct.

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