NCERT Solutions for Maths Class 12 Exercise 4.3

Hello Students! In this post, you will find the complete NCERT Solutions for Maths Class 12 Exercise 4.3.

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NCERT Solutions for Maths Class 12 Exercise 4.1

NCERT Solutions for Maths Class 12 Exercise 4.2

NCERT Solutions for Maths Class 12 Exercise 4.4

NCERT Solutions for Maths Class 12 Exercise 4.5

NCERT Solutions for Maths Class 12 Exercise 4.3

 

Maths Class 12 Ex 4.3 Question 1.

Write the Minors and Cofactors of the elements of following determinants:

Solution:

(i) Let A = 
M₁₁ = Minor of a₁₁ = 3, M₁₂ = Minor of a₁₂ = 0,

M₂₁ = Minor of a₂₁ = –4, M₂₂ = Minor of a₂₂ = 2

Now, cofactors of a_ij is A_ij.

So, A₁₁ = (–1)^{1 + 1} M₁₁ = (–1)² (3) = 3

A₁₂ = (–1)^{1 + 2} M₁₂ = (–1)³ (0) = 0

A₂₁ = (–1)^{2 + 1} M₂₁ = (–1)³ (–4) = 4

A₂₂ = (–1)^{2 + 2} M₂₂ = (–1)⁴ (2) = 2

(ii) Let A = 
M₁₁ = Minor of a₁₁ = d, M₁₂ = Minor of a₁₂ = b,

M₂₁ = Minor of a₂₁ = c, M₂₂ = Minor of a₂₂ = a

Now, cofactors of a_ij is A_ij.

So, A₁₁ = (–1)^{1 + 1} M₁₁ = (–1)² (d) = d

A₁₂ = (–1)^{1 + 2} M₁₂ = (–1)³ (b) = –b

A₂₁ = (–1)^{2 + 1} M₂₁ = (–1)³ (c) = –c

A₂₂ = (–1)^{2 + 2} M₂₂ = (–1)⁴ (a) = a

Maths Class 12 Ex 4.3 Question 2.

Write Minors and Cofactors of the elements of following determinants:

 

Solution:

Maths Class 12 Ex 4.3 Question 3.

Using Cofactors of elements of second row, evaluate

Solution:

The elements of second row are 2, 0 and 1.

Maths Class 12 Ex 4.3 Question 4.

Using Cofactors of elements of third column, evaluate

Solution:

The elements of third column are yz, zx and xy.

Maths Class 12 Ex 4.3 Question 5.

If  and A_ij is Cofactors of a_ij, then value of ∆ is given by
(A) a₁₁ A₃₁ + a₁₂ A₃₂ + a₁₃ A₃₃
(B) a₁₁ A₁₁ + a₁₂ A₂₁ + a₁₃ A₃₁
(C) a₂₁ A₁₁ + a₂₂ A₁₂ + a₂₃ A₁₃
(D) a₁₁ A₁₁ + a₂₁ A₂₁ + a₃₁ A₃₁

Solution:
Option (D) is correct.

Related Links:

NCERT Solutions for Maths Class 12 Exercise 4.1

NCERT Solutions for Maths Class 12 Exercise 4.2

NCERT Solutions for Maths Class 12 Exercise 4.4

NCERT Solutions for Maths Class 12 Exercise 4.5