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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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Chapter 4 Mathematics-I class 12

Exercise 4.2 class 12 Mathematics-I Chapter 4. Determinants

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.

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