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# 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

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

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Chapter 4 Mathematics-I class 12

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

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## 4. Determinants

### | Exercise 4.2 |

## 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.

##### Other Pages of this Chapter: 4. Determinants

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