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# NCERT Solutions class 12 Maths Exercise 4.2

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## 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 [ C1 and C2 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 1st 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.

### 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.

### 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.

## NCERT Solutions class 12 Maths Exercise 4.2

NCERT Solutions Class 12 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 12 Maths includes text book solutions from both part 1 and part 2. NCERT Solutions for CBSE Class 12 Maths have total 20 chapters. 12 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 12 solutions PDF and Maths ncert class 12 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide

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### 14 thoughts on “NCERT Solutions class 12 Maths Exercise 4.2”

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