NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 Determinants
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1: This page consist of detail and accurate NCERT Solutions For Class 12 Maths Chapter 4-Determinants Exercise 4.1 prepared as per the requirements of CBSE board.
Krati Saraswat15 Jan, 2024
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NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 Determinants is prepared by academic team of Physics Wallah. We have prepared NCERT Solutions for all exercise of chapter 4. Given below is step by step solutions of all questions given in NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 Determinants.
NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 Overview
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 covers these important topics. Students are encouraged to review each topic thoroughly in order to fully understand the concepts taught in the chapter and make optimal use of the provided solutions. These solutions are the outcome of the dedicated effort that the Physics Wallah teachers have been doing to aid students in understanding the ideas covered in this chapter. After going over and rehearsing these responses, the goal is for students to easily score outstanding exam results.NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 PDF
Our team of teachers at Physics Wallah has developed thorough solutions for NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 in order to help students understand and apply chapter concepts. The purpose of these questions is to help students comprehend explanations. You may obtain the NCERT Solutions for Class 12 Maths, Chapter 4 PDF by clicking on this link:NCERT Solutions Class 12 Maths Chapter 4 PDF Download Link
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1
Solve The Following Questions of NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 Determinants
Evaluate the following determinants in Exercise 1 and 2. Question 1.
Solution :
= 2(-1) - 4(-5) = -2 + 20 = 18
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.2
Question 2. (i)
(ii)
Solution :
(i)
= (cosθ)(cosθ) - (-sinθ) (sinθ)= cos
2
θ + sin
2
θ= 1
(ii)
= (
x
2
−
x
+ 1)(
x
+ 1) − (
x
− 1)(
x
+ 1)
=
x
3
−
x
2
+
x
+
x
2
−
x
+ 1 − (
x
2
− 1)
=
x
3
+ 1 −
x
2
+ 1
=
x
3
−
x
2
+ 2
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.3
Question
3. If A =
then show that |2A| = 4|A|
then 2A =
2 x
Hence, proved.
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.4
Question 4. If A =
then show that 3|A| = 27|A|
Solution :
Given: A =
then 3A =
3
It can be observed that in the first column, two entries are zero. Thus, we expand along the first column (C
1
) for easier calculation.
Hence, proved.
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5
Question 5. Evaluate the determinants: (i)
(ii)
(iii)
(iv)
Solution :
Evaluate the determinants:
(i) Given:
It can be observed that in the second row, two entries are zero. Thus, we expand along the second row for easier calculation.
=
(ii) Given:
By expanding along the first row, we have:
=
(iii) Given:
Expanding along first row,
=
= 0 + 6 – 6 = 0
(iv) Given:
Expanding along first row,
=
= -10 + 15 = 5
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.6
Question 6. If A =
find |A|
Solution :
Given: A =
Expanding along first row,
=
(ii)
Solution :
(i) Given:
⇒ 2 x 1 - 5 x 4 = 2x * x - 6 x 4
⇒ 2 - 20 = 2x
2
- 24
⇒ 2x
2
= 6
⇒ x
2
= 3
⇒ x = ± √3
(ii)
⇒ 2 x 5 - 4 x 3 = x * 5 - 2x - 3
⇒10 - 12 = 5x - 6x
⇒ - 2 = -x
⇒ x = 2
| NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.1 | NCERT Solutions for Class 12 Maths Chapter 2 Exercise 2.2 |
| NCERT Solutions for Class 12 Maths Chapter 2 Miscellaneous Exercise | |
then x is equal to:
(A) 6
(B) ± 6
(C) - 6
(D) 0
Solution :
Given:
⇒x * x - 18 x 2 = 6 x 6 - 18 x 2
⇒x
2
- 36 = 36 - 36
⇒x
2
- 36 = 0
⇒x = ± 6
Therefore, option (B) is correct.
NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 FAQs
How many exercises are there in determinants?
Class 12 Maths Chapter 4 Determinants has 87 questions in 7 exercises. Practicing these questions ensures an accurate and clear understanding of this topic.
What are the properties of determinants?
There are 10 main properties of determinants: reflection property, all-zero property, proportionality or repetition property, switching property, scalar multiple properties, sum property, invariance property, factor property, triangle property, and co-factor matrix property.
What is determinant and its types?
Determinants are scalar numbers formed by multiplying the elements of a square matrix by their cofactors according to a predefined method.
What is the principle of determinant?
Suppose any two rows or columns of a determinant are interchanged, then its sign changes. If any two rows or columns of a determinant are the same, then the determinant is 0. If any row or column of the determinant is multiplied by a variable k, then its value is multiplied by k.
What is the application of determinants?
Applications of determinants and matrices can be widely seen while checking the consistency of the system of linear equations in two or three variables. We can solve the linear equations in two or three variables using determinants and matrices.
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