Class 12 NCERT Solutions- Mathematics Part I – Chapter 4 Determinants- Exercise 4.2 | Set 2

Chapter 4 Determinants- Exercise 4.2 | Set 1

Question 11. (i)

(ii)

Solution:

(i) L.H.S.=

∵ L.H.S.=R.H.S

Hence proved

(ii)

∵ L.H.S.=R.H.S

Hence proved

Question 12. 

Solution:

∵ L.H.S.=R.H.S

Hence proved

Question 13. 

Solution:

∵ L.H.S.=R.H.S

Hence proved

Question 14. 

Solution:

Multiplying column1,column2,column3  by  a,b,c respectively and then dividing the determinant by  a,b,c .

∵ L.H.S.=R.H.S

Hence proved

Choose the correct answer in Exercises 15 and 16.

Question 15. Let A be a square matrix of order 3 x 3, then|A| is equal to:

(A) k|A|

(B) k²|A|

(C) k³|A|

(D) 3k|A|

Solution:

 Let A = be a square matrix of order 3 x 3   ….(1)

Now, kA=

⇒|kA|=

⇒|kA|=k³

∴ |kA|= k³|A|            [ from eqⁿ .(1) ]

∴ option (C) is correct.

Question 16.Which of 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

Solution:

Since, Determinant is a number which is always associated to a square matrix.

∴ option (C) is correct.