NCERT Solutions for Class 12 Maths Exercise 4.2 Chapter 4 Determinants – FREE PDF Download
NCERT Solutions for Class 12 Maths Chapter 4 – Determinants is a sure-shot way of obtaining the complete marks in the particular chapter for Board Exam 2019- 2020. CoolGyan provides you with Free PDF download of the same solved by Expert Teachers as per NCERT (CBSE) Book guidelines. They provide the students with precise and to the point answers which fetch very good marks in Board Exams. Download today the NCERT CBSE Solutions for Class 12 Maths Chapter 4 – Determinants to achieve your goal score. Class 12 Maths Chapter 4 – Determinants solved by Expert Teachers as per NCERT (CBSE) Book guidelines.
NCERT Solutions for Class 12 Maths Chapter 4 – Determinants
1.Â


OperatingÂ





2.Â
 = 0

OperatingÂ

=Â

=>Â

[

3.Â

operatingÂ

=∣∣∣∣235789637281∣∣∣∣=|276338725981|
=Â

= 9 x 0 = 0 [

4.Â

=Â

OperatingÂ


=Â

=Â


5.Â

operatingÂ

=Â

=Â

=Â

[operatingÂ

=Â

[operatingÂ

=Â

[operatingÂ

=Â

[InterchangingÂ


=Â

[InterchangingÂ


=Â

=Â

6.Â
 = 0

[TakingÂ

=>Â

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









7.Â

Taking commonÂ


=Â

[operatingÂ

=Â

=Â

=Â

=Â


8. (i)Â
(ii)Â



=Â

∣∣∣∣∣100ab−ac−aa2(b−a)(b+a)(c−a)(c+a)∣∣∣∣∣|1aa20b−a(b−a)(b+a)0c−a(c−a)(c+a)|
Taking (b-a) and (c-a) common from R2Â and R3Â respectively.
=(b−a)(c−a)∣∣∣∣∣100a11a2(b+a)(c+a)∣∣∣∣∣=(b−a)(c−a)|1aa201(b+a)01(c+a)|
R2→R2−R3R2→R2−R3
=(b−a)(c−a)∣∣∣∣∣100a01a2(b−c)(c+a)∣∣∣∣∣=(b−a)(c−a)|1aa200(b−c)01(c+a)|
[Expanding along 1st column]
=(b−a)(c−a)∣∣∣01(b+a)(c+a)∣∣∣=(b−a)(c−a)|0(b+a)1(c+a)|
=(b−a)(c−a)(0−(b−c))=(b−a)(c−a)(0−(b−c))
=(b−a)(c−a)(c−b)=(b−a)(c−a)(c−b)
=Â

(ii)Â L.H.S. =Â

operatingÂ


=Â

=Â

=Â

=Â

=Â Â

=Â

=Â

=Â

=Â

=Â

9.Â

L.H.S. =Â

[MultiplyingÂ


=1xyz∣∣∣∣∣x2y2z2x3y3z3xyzxyzxyz∣∣∣∣∣=1xyz|x2x3xyzy2y3xyzz2z3xyz|
=Â

Taking xyz commong from C3
=Â

=Â

[operatingÂ

=Â

=Â

=Â

=Â

=Â

=Â

=Â

=Â

=Â

=Â

=Â

=Â

10. (i)Â
(ii)Â


=Â

Taking 5x+4 common from R1
=Â

[operatingÂ


=Â

=Â

=Â

(ii)Â L.H.S. =Â


=Â

Taking 3y+k common from C1
=Â

[operatingÂ


=Â

=Â

=Â


= R.H.S. Proved.
11. (i)Â
(ii)Â


=Â

Taking a+b+c common from R1
=Â


=Â

=Â

=Â

=Â

(ii)Â L.H.S. =Â


=Â

Taking 2(x+y+z) common from C1
=Â


=Â

=Â

=Â

=Â

12.Â


=Â

Taking 1+x+x2Â common from R1
=Â


=Â

=Â

=Â

=Â

=Â

=Â

=Â

=Â

=Â

13.Â


=Â

=Â


=Â

=Â

=Â

=Â

14.Â

MultiplyingÂ



=Â

Taking a,b, and c common from R1, R2 and R3 respectively.
=Â


=Â

=Â


=Â

=Â

=Â

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)Â
(B)Â
(C)Â
(D)Â







=Â

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.
Therefore, option (C) is correct.