NCERT Solutions class 12 Maths Exercise 4.2

NCERT Solutions class 12 Maths Exercise 4.2 Class 12 Maths book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 12 Maths chapter wise NCERT solution for Maths part 1 and Maths part 2 for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.

Download NCERT solutions for Determinants  as PDF

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.

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2.

Ans. On  Operating

=

=  = 0 = R.H.S.

[ All entries of one column here first are zero]

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3.  

Ans. On  operating

=  =

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

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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.

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6.

Ans. Let

=  [Taking  common from each row]

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

 

 

  Proved.

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7.  

Ans. L.H.S. =

Taking common  from  respectively,

=

=    [operating ]

=  =

=  =  = R.H.S.

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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.

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9.  

Ans.

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

=  =

=  [operating ]

=

=

=

=

=

=

=

=

=

=

=  = R.H.S.

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10. (i)  

(ii)  

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

=  

=

= [operating  and ]

=

=  = R.H.S.

(ii) L.H.S. =

=  

=

=  [operating  and ]

=

=  =

= R.H.S.  Proved.

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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.

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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.

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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.

NCERT Solutions class 12 Maths Exercise 4.2

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