## NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.2 (Ex 4.2)

Free PDF download of NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.2 (Ex 4.2) and all chapter exercises at one place prepared by expert teacher as per NCERT (CBSE) books guidelines. Class 12 Maths Chapter 4 Determinants Exercise 4.2 Questions with Solutions to help you to revise complete Syllabus and Score More marks.

## NCERT Solutions class 12 Maths Determinants

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

**1. **

**Ans. **Given:

Operating

0 = 0 [ C_{1} and C_{2} are identical]

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

**2. **

**Ans. **On Operating

=

= = 0 = R.H.S.

[ All entries of one column here first are zero]

**3. **

**Ans. **On operating

= =

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

**4. **

**Ans. **Given: =

Operating

=

= = 0 [ two columns are identical] Proved.

**5. **

**Ans. **L.H.S. = operating

=

=

=

= [operating ]

= [operating ]

= [operating ]

= [Interchanging and ]

= [Interchanging and ]

= = R.H.S.

**6. **

**Ans. **Let

= [Taking common from each row]

Interchanging rows and columns in the determinants on R.H.S.,

Proved.

**7. **

**Ans. **L.H.S. =

Taking common from respectively,

=

= [operating ]

= =

= = = R.H.S.

**8. (i) **

**(ii) **

**Ans. (i) **L.H.S. = operating and ,

=

= [Expanding along 1^{st} column]

=

=

= = = R.H.S. Proved.

**(ii) **L.H.S. = operating and

=

=

=

=

=

=

=

=

=

= = R.H.S.

**9. **

**Ans. **

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

= =

= [operating ]

=

=

=

=

=

=

=

=

=

=

= = R.H.S.

**10. (i) **

**(ii) **

**Ans. (i) **L.H.S. =

=

=

= [operating and ]

=

= = R.H.S.

**(ii) **L.H.S. =

=

=

= [operating and ]

=

= =

= R.H.S. Proved.

**11. (i) **

**(ii) **

**Ans. (i)** L.H.S. =

=

=

=

=

=

= = R.H.S. Proved.

**(ii)** L.H.S. =

=

=

=

=

=

= = R.H.S. Proved.

**12. **

**Ans. **L.H.S. =

=

=

=

=

=

=

=

=

=

=

= = R.H.S. Proved.

**13. **

**Ans. **L.H.S. =

=

=

=

=

=

= = R.H.S.

**14. **

**Ans. **L.H.S. =

Multiplying by respectively and then dividing the determinant by

=

=

=

=

=

=

= = R.H.S. Proved.

### NCERT Solutions class 12 Maths Exercise 4.2

**Choose the correct answer in Exercises 15 and 16.**

**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)]

Therefore, option (C) is correct.

### NCERT Solutions class 12 Maths Exercise 4.2

**16. Which is the following is correct:**

**(A) Determinant is a square matrix.**

**(B) Determinant is a number associated to a matrix.**

**(C) Determinant is a number associated to a square matrix.**

**(D) None of these.**

**Ans. **Since, Determinant is a number associated to a square matrix.

Therefore, option (C) is correct.

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