JEE Exam > JEE Notes > Mathematics (Maths) Class 12 > NCERT Solutions Exercise 4.2: Determinants
NCERT Solutions Exercise 4.2: Determinants | Mathematics (Maths) Class 12 - JEE PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer Page 2 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer XII Here, the two rows R1 and R3 are identical. ? = 0. Question 3: Using the property of determinants and without expanding, prove that: Answer Question 4: Using the property of determinants and without expanding, prove that: Answer Page 3 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer XII Here, the two rows R1 and R3 are identical. ? = 0. Question 3: Using the property of determinants and without expanding, prove that: Answer Question 4: Using the property of determinants and without expanding, prove that: Answer By applying C3 ? C3 + C2, we have: Here, two columns C1 and C3 are proportional. ? = 0. Question 5: Using the property of determinants and without expanding, prove that: Answer Applying R2 ? R2 - R3, we have: Page 4 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer XII Here, the two rows R1 and R3 are identical. ? = 0. Question 3: Using the property of determinants and without expanding, prove that: Answer Question 4: Using the property of determinants and without expanding, prove that: Answer By applying C3 ? C3 + C2, we have: Here, two columns C1 and C3 are proportional. ? = 0. Question 5: Using the property of determinants and without expanding, prove that: Answer Applying R2 ? R2 - R3, we have: Applying R1 ?R3 and R2 ?R3, we have: Applying R1 ? R1 - R3, we have: Applying R1 ?R2 and R2 ?R3, we have: From (1), (2), and (3), we have: Page 5 Exercise 4.2 Question 1: Using the property of determinants and without expanding, prove that: Answer Question 2: Using the property of determinants and without expanding, prove that: Answer XII Here, the two rows R1 and R3 are identical. ? = 0. Question 3: Using the property of determinants and without expanding, prove that: Answer Question 4: Using the property of determinants and without expanding, prove that: Answer By applying C3 ? C3 + C2, we have: Here, two columns C1 and C3 are proportional. ? = 0. Question 5: Using the property of determinants and without expanding, prove that: Answer Applying R2 ? R2 - R3, we have: Applying R1 ?R3 and R2 ?R3, we have: Applying R1 ? R1 - R3, we have: Applying R1 ?R2 and R2 ?R3, we have: From (1), (2), and (3), we have: Hence, the given result is proved. Question 6: By using properties of determinants, show that: Answer We have, Here, the two rows R1 and R3 are identical. ? = 0.Read More
|
204 videos|290 docs|139 tests
|
FAQs on NCERT Solutions Exercise 4.2: Determinants - Mathematics (Maths) Class 12 - JEE
| 1. What is a determinant? |  |
Ans. A determinant is a scalar value that can be calculated from a square matrix. It is used in various mathematical calculations, including solving systems of equations, finding inverses of matrices, and determining whether a matrix is invertible or singular. The determinant is calculated by summing the products of the elements of a matrix in a specific pattern.
| 2. How do you calculate the determinant of a 2x2 matrix? | |
Ans. To calculate the determinant of a 2x2 matrix, you need to subtract the product of the top left and bottom right elements from the product of the top right and bottom left elements. So, if the matrix is [a b; c d], the determinant is ad - bc.
| 3. What is the significance of the determinant of a matrix? | |
Ans. The determinant of a matrix has several important applications in mathematics and physics. One of the most significant applications is in solving systems of linear equations. If the determinant of a matrix is zero, it means that the matrix is singular and the system of equations has no unique solution. If the determinant is non-zero, the system has a unique solution. Additionally, the determinant is used to find the inverse of a matrix, which is useful in many applications.
| 4. Can the determinant of a matrix be negative? | |
Ans. Yes, the determinant of a matrix can be negative. The sign of the determinant depends on the order of the rows and columns of the matrix. Specifically, if you swap two rows or columns of a matrix, the sign of the determinant changes. If the number of row/column swaps is odd, the determinant is negative, and if it is even, the determinant is positive. So, even if all elements of a matrix are positive, the determinant can still be negative.
| 5. What is the relationship between the determinant of a matrix and its eigenvalues? | |
Ans. The determinant of a matrix is equal to the product of its eigenvalues. The eigenvalues of a matrix are the values of λ that satisfy the equation Ax = λx, where x is a non-zero vector. The determinant can be used to find the eigenvalues of a matrix, which is useful in many applications, including quantum mechanics and structural engineering. Additionally, the determinant can be used to determine whether a matrix is positive definite, which is important in optimization problems.
Related Exams
About this Document
|
1.9K Views |
|
4.93/5 Rating |
|
Dec 22, 2024 Last updated |
Document Description: NCERT Solutions Exercise 4.2: Determinants for JEE 2024 is part of Mathematics (Maths) Class 12 preparation.
The notes and questions for NCERT Solutions Exercise 4.2: Determinants have been prepared according to the JEE exam syllabus. Information about NCERT Solutions Exercise 4.2: Determinants covers topics
like and NCERT Solutions Exercise 4.2: Determinants Example, for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for NCERT Solutions Exercise 4.2: Determinants.
Introduction of NCERT Solutions Exercise 4.2: Determinants in English is available as part of our Mathematics (Maths) Class 12
for JEE & NCERT Solutions Exercise 4.2: Determinants in Hindi for Mathematics (Maths) Class 12 course.
Download more important topics related with notes, lectures and mock test series for JEE
Exam by signing up for free. JEE: NCERT Solutions Exercise 4.2: Determinants | Mathematics (Maths) Class 12 - JEE
Description
Full syllabus notes, lecture & questions for NCERT Solutions Exercise 4.2: Determinants | Mathematics (Maths) Class 12 - JEE - JEE | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 12 | Best notes, free PDF download
Information about NCERT Solutions Exercise 4.2: Determinants
In this doc you can find the meaning of NCERT Solutions Exercise 4.2: Determinants defined & explained in the simplest way possible. Besides explaining types of
NCERT Solutions Exercise 4.2: Determinants theory, EduRev gives you an ample number of questions to practice NCERT Solutions Exercise 4.2: Determinants tests, examples and also practice JEE
tests
|
Explore Courses for JEE exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
past year papers
,Objective type Questions
,mock tests for examination
,Free
,shortcuts and tricks
,Extra Questions
,MCQs
,NCERT Solutions Exercise 4.2: Determinants | Mathematics (Maths) Class 12 - JEE
,video lectures
,NCERT Solutions Exercise 4.2: Determinants | Mathematics (Maths) Class 12 - JEE
,Previous Year Questions with Solutions
,Viva Questions
,NCERT Solutions Exercise 4.2: Determinants | Mathematics (Maths) Class 12 - JEE
,study material
,Semester Notes
,ppt
,Summary
,Sample Paper
,Important questions
,practice quizzes
,Exam
;
Additional Information about NCERT Solutions Exercise 4.2: Determinants for JEE Preparation
NCERT Solutions Exercise 4.2: Determinants Free PDF Download
The NCERT Solutions Exercise 4.2: Determinants is an invaluable resource that delves deep into the core of the JEE exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the NCERT Solutions Exercise 4.2: Determinants now and kickstart your journey towards success in the JEE exam.
Importance of NCERT Solutions Exercise 4.2: Determinants
The importance of NCERT Solutions Exercise 4.2: Determinants cannot be overstated, especially for JEE aspirants.
This document holds the key to success in the JEE exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
NCERT Solutions Exercise 4.2: Determinants Notes
NCERT Solutions Exercise 4.2: Determinants Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to NCERT Solutions Exercise 4.2: Determinants.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, NCERT Solutions Exercise 4.2: Determinants Notes on EduRev are your ultimate resource for success.
NCERT Solutions Exercise 4.2: Determinants JEE Questions
The "NCERT Solutions Exercise 4.2: Determinants JEE Questions" guide is a valuable resource for all aspiring students preparing for the
JEE exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study NCERT Solutions Exercise 4.2: Determinants on the App
Students of JEE can study NCERT Solutions Exercise 4.2: Determinants alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the NCERT Solutions Exercise 4.2: Determinants,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of NCERT Solutions Exercise 4.2: Determinants is prepared as per the latest JEE syllabus.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup