NCERT Solutions Class 12

NCERT Solutions Class 12

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

 Exercise 4.4

1. Write minors and cofactors of the elements of the following determinants:

(i) 

(ii) 

Ans. (i) Let 

M11 = Minor of  and A11 = 

M12 = Minor of  and A12 = 

M21 = Minor of  and A21 = 

M22 = Minor of  and A22 = 

(ii) Let 

M11 = Minor of  and A11 = 

M12 = Minor of  and A12 = 

M21 = Minor of  and A21 = 

M22 = Minor of  and A22 = 


 

2. Write minors and cofactors of the elements of the following determinants:

(i) 

(ii)  

Ans. (i) Let 

M11 = Minor of  and A11 = 

M12 = Minor of  and A12 = 

M13 = Minor of  and A13 = 

M21 = Minor of  and A21 = 

M22 = Minor of  and A22 = 

M23 = Minor of  and A23 = 

M31 = Minor of  and A31 = 

M32 = Minor of  and A32 = 

M33 = Minor of  and A31 = 

(ii) Let 

M11 = Minor of  and A11 = 

M12 = Minor of  and A12 = 

M13 = Minor of  and A13 = 

M21 = Minor of  and A21 = 

M22 = Minor of  and A22 = 

M23 = Minor of  and A23 = 

M31 = Minor of  and A31 = 

M32 = Minor of  and A32 = 

M33 = Minor of  and A31 = 


 

3. Using cofactors of elements of second row, evaluate: 

Ans. Elements of second row of  are 

A21 = Cofactor of  = 

A22 = Cofactor of  = 

A23 = Cofactor of  = 

  = 


 

4. Using cofactors of elements of third column, evaluate: 

Ans. Elements of third column of  are 

A13 = Cofactor of  = 

A23 = Cofactor of  = 

A33 = Cofactor of  = 

  = 

 = 

 = 

 = 

 = 


 

5. If  and  is cofactor of  then value of  is given by:

(A) 

(B)  

(C) 

(D)  

Ans. Option (D) is correct.

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