## NCERT Solutions for Class 12 Maths Exercise 4.4 Chapter 4 Determinants â€“ FREE PDF Download

NCERT Solutions for Class 12 Maths Chapter 4 â€“ Determinants is a sure-shot way of obtaining the complete marks in the particular chapter for Board Exam 2019- 2020. CoolGyan provides you with Free PDF download of the same solved by Expert Teachers as per NCERT (CBSE) Book guidelines. They provide the students with precise and to the point answers which fetch very good marks in Board Exams. Download today the NCERT CBSE Solutions for Class 12 Maths Chapter 4 â€“ Determinants to achieve your goal score. Class 12 Maths Chapter 4 â€“ Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.

# NCERT Solutions for Class 12 Maths Chapter 4 â€“ Determinants

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

(i)Â

(ii)Â

M

M

M

M

(ii)Â LetÂ

M

M

M

M

(i)Â

(ii)Â

**Ans.**Â (i)Â LetÂ

M

_{11}Â = Minor ofÂ Â and A

_{11}Â =Â

M

_{12}Â = Minor ofÂ Â and A

_{12}Â =Â

M

_{21}Â = Minor ofÂ a21=|âˆ’4|=âˆ’4a21=|âˆ’4|=âˆ’4Â Â and A

_{21}Â =Â

M

_{22}Â = Minor ofÂ Â and A

_{22}Â =Â

(ii)Â LetÂ

M

_{11}Â = Minor ofÂ Â and A

_{11}Â =Â

M

_{12}Â = Minor ofÂ Â and A

_{12}Â =Â

M

_{21}Â = Minor ofÂ Â and A

_{21}Â =Â

M

_{22}Â = Minor ofÂ Â and A

_{22}Â =Â

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

(i)Â

(ii)Â

**Ans.**Â (i)Â LetÂ

M

_{11}Â = Minor ofÂ Â and A

_{11}Â =Â

M

_{12}Â = Minor ofÂ Â and A

_{12}Â =Â

M

_{13}Â = Minor ofÂ Â and A

_{13}Â =Â

M

_{21}Â = Minor ofÂ Â and A

_{21}Â =Â

M

_{22}Â = Minor ofÂ Â andÂ A

_{22}Â =Â

M

_{23}Â = Minor ofÂ Â andÂ A

_{23}Â =Â

M

_{31}Â = Minor ofÂ Â andÂ A

_{31}Â =Â

M

_{32}Â = Minor ofÂ Â andÂ A

_{32}Â =Â

M

_{33}Â = Minor ofÂ Â andÂ A

_{31}Â =Â

(ii)Â LetÂ

M

_{11}Â = Minor ofÂ Â and A

_{11}Â =Â

M

_{12}Â = Minor ofÂ Â and A

_{12}Â =Â

M

_{13}Â = Minor ofÂ Â and A

_{13}Â =Â

M

_{21}Â = Minor ofÂ Â and A

_{21}Â =Â

M

_{22}Â = Minor ofÂ Â and A

_{22}Â =Â

M

_{23}Â = Minor ofÂ Â and A

_{23}Â =Â

M

_{31}Â = Minor ofÂ Â and A

_{31}Â =Â

M

_{32}Â = Minor ofÂ Â and A

_{32}Â =Â

M

_{33}Â = Minor ofÂ Â and A

_{31}Â =Â

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

**Ans.**Â Elements of second row ofÂ Â areÂ

A

_{21}Â = Cofactor ofÂ Â =Â

A

_{22}Â = Cofactor ofÂ Â =Â

A

_{23}Â = Cofactor ofÂ Â =Â

Â Â =Â

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

**Ans.**Â Elements of third column ofÂ Â areÂ

A

_{13}Â = Cofactor ofÂ Â =Â

A

_{23}Â = Cofactor ofÂ Â =Â

A

_{33}Â = Cofactor ofÂ Â =Â

Â Â =Â

=Â Â =Â

=Â Â =Â

=Â Â =Â

=Â Â =Â

### 5. IfÂ Â andÂ Â is cofactor ofÂ Â then value ofÂ Â is given by:

(A)Â

(B)Â

(C)Â

(D)Â

**Ans.**Â Option (D) is correct.