NCERT Solutions for Maths Class 12 Exercise 4.2

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Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

NCERT Solutions for Maths Class 12 Exercise 4.2 helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

All the schools affiliated with CBSE, follow the NCERT books for all subjects. You can check your syllabus from NCERT Syllabus for Mathematics Class 12.

NCERT Solutions for Maths Class 12 Exercise 4.2 are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

If you want to recall All Maths Formulas for Class 12, you can find it by clicking this link.
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NCERT Solutions for Maths Class 12 Exercise 4.1
NCERT Solutions for Maths Class 12 Exercise 4.3
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 4.6

NCERT Solutions for Maths Class 12 Exercise 4.2

Using the property of determinants and without expanding in Questions 1 to 5, prove that:

Maths Class 12 Ex 4.2 Question 1.

Solution:

[Here, in the first determinant, C₁ = C₃ and in the second determinant, C₂ = C₃. Therefore, the value of each of the determinants is equal to zero.]
= 0 + 0
= 0
= R.H.S.

Maths Class 12 Ex 4.2 Question 2.

Solution:

Maths Class 12 Ex 4.2 Question 3.

Solution:

Maths Class 12 Ex 4.2 Question 4.

Solution:

[Since, C₁ and C₃ are proportional, therefore the value of this determinant is 0.]

= 0

= R.H.S.

Maths Class 12 Ex 4.2 Question 5.

Solution:

By using properties of determinants in Questions 6 to 14, show that:

Maths Class 12 Ex 4.2 Question 6.

Solution:

[Since the rows R₁ and R₃ are the same.]

Maths Class 12 Ex 4.2 Question 7.

Solution:

Maths Class 12 Ex 4.2 Question 8.

Solution:

Maths Class 12 Ex 4.2 Question 9.

Solution:

Maths Class 12 Ex 4.2 Question 10.

Solution:

Maths Class 12 Ex 4.2 Question 11.

Solution:

Maths Class 12 Ex 4.2 Question 12.

Solution:

Maths Class 12 Ex 4.2 Question 13.

Solution:

Maths Class 12 Ex 4.2 Question 14.

Solution:

Maths Class 12 Ex 4.2 Question 15.

Let A be a square matrix of order 3 × 3, then |kA| is equal to
(A) k|A| (B) k²|A| (C) k³|A| (D) 3k|A|

Solution:

Hence, option (C) is correct.

Maths Class 12 Ex 4.2 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:
We know that to every square matrix, A = [a_ij] of order n, we can associate a number called the determinant of square matrix A, where a_ij= (i, j)^th element of A.

Thus, the determinant is a number associated to a square matrix.

Hence, option (C) is correct.

NCERT Solutions for Maths Class 12 Exercise 4.1
NCERT Solutions for Maths Class 12 Exercise 4.3
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 4.6

NCERT Solutions for Maths Class 12 Exercise 4.2