RBSE Solutions for Class 12 Maths Chapter 4 Determinants Ex 4.2

Rajasthan Board RBSE Class 12 Maths Chapter 4 Determinants Ex 4.2

RBSE Solutions For Class 12 Maths Chapter 4 Question 1.
RBSE Solutions For Class 12 Maths Chapter 4 Determinants, then find l : m.
Solution:
RBSE Solutions for Class 12 Maths Chapter 4 Determinants
⇒ l x 3 – 2 x m = 0
⇒ 3l – 2m= 0
⇒ 3l = 2m
⇒ \(\frac { l }{ m }\) = \(\frac { 2 }{ 3 }\)
So, l : m = 2 : 3

RBSE Solutions For Class 12 Maths Chapter 4 Miscellaneous Question 2.
Find the minors of elements of second row of determinant
RBSE Solutions for Class 12 Maths Chapter 4 Determinants .
Solution:
Ex 4.2 Class 12 Determinants RBSE

Ex 4.2 Class 12 Question 3.
Find the value of determinant
Exercise 4.2 Class 12 Determinants RBSE
Solution:
RBSE Solutions For Class 12 Maths Chapter 4 Determinants

Maths RBSE Solutions Class 7 Chapter 4 Exercise 4.2 Question 4.
Write the effect on value of determinant, if first and third columns of any determinant are interchanged.
Solution:
Sign of determinant will be changed.

Question 5.
Prove that
Ex 4.2 Class 12 Maths Determinants
Solution:
Class 12 Maths Exercise 4.2 Determinants

RBSE Solutions For Class 10 Maths Chapter 4.2 Question 6.
Find the value of determinant
Class 12 Maths Determinants Exercise 4.2 Determinants.
Solution:
Determinants Class 12 Determinants RBSE Class 12 Maths Chapter 4 Solutions Determinants

Exercise 4.2 Class 12 Question 7.
Solve the equation :
Class 12 Determinants Solutions RBSE
Solution:
Determinants Solutions Class 12 RBSE
Ex 4.2 Class 10 RBSE Determinants
Now, according to question, changed form of given eq.
i.e., eq. (i) is equal to zero.
img
⇒ 1(- 145 + 143) – 1(- 58 + 13x + 104) + 2( – 22 – 5x +40) = 0
– 2 + 13x – 46 – 10x + 36 = 0
⇒ 3x – 12 = 0
⇒ \(\frac { 12 }{ 3 }\) = 4.

RBSE Solutions For Class 12 Maths Chapter 4 Question 8.
Prove without expansion that,
Class 12 Maths RBSE Solution Chapter 2 Determinants
Solution:
Let
4.2 Class 12 Determinants
Class 12 Maths Ex 4.2 Determinants

RBSE Solutions Class 7 Maths Chapter 4 Exercise 4.2 Question 9.
Prove that,
4.2 Maths Class 12
Solution:
RBSE Solutions For Class 12 Hindi Sarjana
Exercise 4.2 Class 12 Maths Solutions
= (a + b + c)[0 – 0 + 1{(a – c)(b – c) – (a – b) (b – a)}]
= (a + b + c){(ab – ca – bc + c2) – (ab – a2 – b2 + ab)}
= (a + b + c)(ab – ca – bc + c2 – ab + a2 + b2 – ab)
= (a + b + c)(a2 + b2 + c2 – ab – bc – ca)
= a3 + b3 + c3 – 3abc – R.H.S. Proved

RBSE Solutions For Class 12 Maths Chapter 2 Question 10.
Find
Ch4 Maths Class 10 Determinants
Solution:
RBSE Solution Class 12 Maths Chapter 2 Determinants

Ex 4.2 Class 12 Maths Question 11.
If ω is a cube root, then find
Ex4.2 Class 12 Determinants
Solution:
Exercise 4.2 Maths Class 12 Determinants
= 1(1 – ω2) – 1(1 – ω3) + ω2(ω – ω2)
= 1 – ω2 – 1 + ω3 + ω3 – ω4
= 1 – ω2 – 1 + 1 + 1 – ω3.ω (∵ ω3 = 1)
= 3 – ω2 – 1 – ω (∵ ω3 = 1)
= 3 – (1 + ω + ω2) = 3 – 0 = 3 (∵ 1 + ω + ω2 = 0)

Class 12 Maths Exercise 4.2 Question 12.
Prove that
Class 12 Maths Ch 4 Ex 4.2 Determinants
Solution:
Class 12 Maths Ex 4.2 Solutions Determinants
Exercise 4.2 Class 12 Maths Determinants

Class 12 Maths Determinants Exercise 4.2 Question 13.
If in determinant img, A1, B1, C1, ……….. etc are co-factors of elements a1, b1, C1, … respectively, then prove that :
Class 12 Determinants Exercise 4.2 Determinants
Solution:
Determinants Ex 4.2 Solutions Determinants
Determinants Class 12 Ex 4.2 Determinants

RBSE Solutions for Class 12 Maths