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# NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.1 Determinants - PDF Download

NCERT solutions for class 12 maths chapter 4 exercise 4.1 Determinants is based on finding the determinant of the square matrix. In this exercise, you will also learn the determinant of matrix of order one, determinant of a matrix of order two and determinant of a matrix of order 3x3. A scalar quantity is the value of the determinant that is dependent on certain properties and parameters of linear algebra.

Class 12 maths chapter 4 exercise 4.1 NCERT solutions has a total of 8 questions related to finding the value of determinants of square matrix of given order. Students may find the concept of determinants to be complex at first, but with the extensive practice of questions given in NCERT solutions for ex 4.1 class 12 maths chapter 4 by eSaral's subject matter specialists, all the confusion and doubt can be eliminated. These solutions can be downloaded in PDF format from the official website of eSaral to practice questions of exercise 4.1. Students can prepare for their board exams as well by practicing from these solution PDFs. You can download the free PDF of NCERT solutions from the link mentioned below.

## Topics Covered in Exercise 4.1 Class 12 Mathematics Questions

Ex 4.1 class 12 maths solutions describes the topic of determinants with proper explanation. Here, you can find in-depth knowledge of determinants of a matrix of order one, determinant of a matrix of order two and determinant of a matrix of order 3 × 3 which are elaborated by the experienced teachers of eSaral.

 1 Determinant Determinant of a matrix of order one Determinant of a matrix of order two Determinant of a matrix of order 3 × 3
1. Determinant - To every square matrix A of order n, we can associate a number (real or complex) called determinant of the square matrix A.

(i) For matrix A, |A| is read as the determinant of A and not the modulus of A.

(ii) Only square matrices have determinants.

In this section, you will learn some of the essential order of defining determinants.

• Determinant of a matrix of order one

Let say A = [a ] be the matrix of order 1, then the determinant of A is defined to be equal to a.

• Determinant of a matrix of order two

If you have a matrix of order 2 × 2, then the determinant of the matrix is A.

Where A is $\mathrm{A}=\left[\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right]$

So the determinant of A is defined as:

det (A) = |A| = ∆ = $\left|\begin{array}{ll}a_{11} & a_{12} \\ a_{21} & a_{22}\end{array}\right|=a_{11} a_{22}-a_{21} a_{12}$

• Determinant of a matrix of order 3 × 3

Determinant of a matrix of order three can be determined by expressing it in terms of second order determinants. This is known as expansion of a determinant along a row (or a column). There are six ways of expanding a determinant of order 3 corresponding to each of three rows (R1 , R2 and R3 ) and three columns (C1 , C2 and C3 ) giving the same value.

You will get the detailed explanation of determinant of a matrix of order 3x3 in NCERT textbook for class 12 maths chapter 4 ex 4.1.

## Tips for Solving Exercise 4.1 Class 12 Chapter 4 Determinants

Ex 4.1 class 12 maths ch 4 has questions related to determinants which can be solved by going through the tips and techniques provided by subject experts of eSral.

1. Students will easily understand all of the fundamental concepts if they thoroughly practice all of the problems in the NCERT solutions for class 12 maths chapter 4 Determinants exercise 4.1.

2. One of the simplest ways to understand all the main topics is to read all the important notes that are included along with practice problems in NCERT solutions class 12 maths chapter 4 ex 4.1. Students that study according to topics will also be able to do well in board exams.

3. It is advised to follow the illustrative format of questions of ex 4.1 class 12 math solutions for chapter 4, as it provides deep understanding of difficult topics of ex 4.1.

## Importance of Solving Ex 4.1 Class 12 Maths Chapter 4 Determinants

You will get a lot of benefits by solving ex 4.1 class 12 maths chapter 4 determinants. Here, you can check some of them which are mentioned below.

1. Students can get conceptual understanding of determinants by solving questions provided in NCERT solutions class 12 maths chapter 4 ex 4.1.

2. Ex 4.1 class 12 maths chapter 4 solutions have provided answers of questions in stepwise and detailed manner so you can comprehend the concept clearly.

3. These solutions will help you in revising the topics and questions before final exams to score good marks.

4. You can also cross check your answer by NCERT solutions PDF of ex 4.1 to be more confident in exams.

Question 1. What is determinant in NCERT solutions class 12 maths chapter 4 ex 4.1?

Answer 1. A scalar value of a square matrix which characterizes some properties of the matrix is known as a determinant.

Question 2. How many types are described to find the determinant of the square matrix in ex 4.1 class 12 maths chapter 4?

Answer 2. You can find three types to find the determinant of a square matrix.

1. Determinant of a matrix of order one

2. Determinant of a matrix of order two

3. Determinant of a matrix of order 3 × 3