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Solutions ⇒ Class 12th ⇒ Mathematics-I ⇒ 4. Determinants

# Solutions 4. Determinants - Exercise 4.2 | Class 12 Mathematics-I - Toppers Study

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## Solutions 4. Determinants - Exercise 4.2 | Class 12 Mathematics-I - Toppers Study

CBSE board students who preparing for class 12 ncert solutions maths and Mathematics-I solved exercise chapter 4. Determinants available and this helps in upcoming exams 2023-2024.

### You can Find Mathematics-I solution Class 12 Chapter 4. Determinants

• All Chapter review quick revision notes for chapter 4. Determinants Class 12
• NCERT Solutions And Textual questions Answers Class 12 Mathematics-I
• Extra NCERT Book questions Answers Class 12 Mathematics-I
• Importatnt key points with additional Assignment and questions bank solved.

Chapter 4 Mathematics-I class 12

### Exercise 4.2 class 12 Mathematics-I Chapter 4. Determinants

• Solutions 4. Determinants - Exercise 4.2 | Class 12 Mathematics-I - Toppers Study
• Class 12 Ncert Solutions
• Solution Chapter 4. Determinants Class 12
• Solutions Class 12
• Chapter 4. Determinants Exercise 4.2 Class 12

## Solutions 4. Determinants - Exercise 4.2 | Class 12 Mathematics-I - Toppers Study

Exercise - 4.2

Using the properties of determinants and without expanding in Exercise 1 to 5, prove that:

Ques.1.

Ans. Given:

Operating

0 = 0 [ C1 and C2 are identical]

L.H.S. = R.H.S.

hance proved.

Ques.2.

Ans. On  Operating

= 0 = R.H.S.

[ All entries of one column here first are zero]

hance proved.

Ques.3.

Ans. On  operating

=

= 9 x 0 = 0 [ two columns are identical]

hance Proved.

Ques.4.

Ans. Given:      =

Operating

= 0 [ two columns are identical]

hance Proved.

Ques.5.

Ans. L.H.S. =  operating

[operating ]

[operating ]

[operating ]

[Interchanging  and ]

[Interchanging  and ]

= R.H.S.

hance proved.

Using the properties of determinants and with expanding in Exercise 6 to 14, prove that:

Ques.6.

Ans. Let

[Taking  common from each row]

Interchanging rows and columns.,

hance Proved.

Ques.7.

Ans. L.H.S. =

Taking common  from  respectively,

[operating ]

=

=  = R.H.S.

hance proved.

Ques.8. (i)

(ii)

Ans. (i) L.H.S. =  operating  and ,

[Expanding along 1st column]

=  = R.H.S.

hance Proved.

(ii) L.H.S. =  operating  and

=

= R.H.S.

hance proved.

Ques.9.

Ans.

L.H.S. =  =  [Multiplying  by  respectively]

=

[operating ]

= R.H.S.

hance proved.

Ques.10. (i)

(ii)

Ans. (i) L.H.S. =

[operating  and ]

= R.H.S.

hance proved.

(ii) L.H.S. =

[operating  and ]

=

= R.H.S.

hance Proved.

Ques.11. (i)

(ii)

Ans. (i) L.H.S. =

= R.H.S.

hance Proved.

(ii) L.H.S. =

= R.H.S.

hance Proved.

Ques.12.

Ans. L.H.S. =

= R.H.S.

hance Proved.

Ques.13.

Ans. L.H.S. =

= R.H.S.

Ques.14.

Ans. L.H.S. =

Multiplying  by  respectively and then dividing the determinant by

= R.H.S.

hance, proved.

Choose the correct answer in Exercises 15 and 16.

Ques.15. Let A be a square matrix of order 3 x 3, then  is equal to:

(A)

(B)

(C)

(D)

Ans. Let A =  be a square matrix of order 3 x 3.   ……….(i)

[From eq. (i)]

hance, option (C) is correct.

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## Study Materials List:

##### Solutions ⇒ Class 12th ⇒ Mathematics-I
1. Relations and Functions
2. Inverse Trigonometric Functions
3. Matrices
4. Determinants
5. Continuity And Differentiability
6. Application of Derivatives

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