NCERT Solutions for Class 12 Maths Chapter 4- Determinants Exercise 4.5 is a precise yet handy solution when it comes to understanding the problems in Exercise 4.5 in detail. They have been prepared by subject matter experts to aid you in your study process.Â Exercise 4.5 Class 12 Maths Solution has been developed on the basis of guidelines drafted by the CBSE. Get the Exercise 4.5 Class 12 Maths NCERT Solutions available as free PDF downloads by Vedantu to enhance your exam preparation.Â Â
Class 12 is a very vital year in your academic life. It literally decides which education path you will choose. Class 12 board exams are crucial for everyone. They stay with you wherever you go. The subjects you learn in Class 12 will also help you build a solid conceptual foundation for your graduation and post-graduation years. Thorough preparation for Class 12 exams will also help you succeed in different competitive exams.
Class 12 Maths Chapter 4 Exercise 4.5 deals with Adjoint and Inverse of a Matrix. Exercise 4.5 Class 12 Maths consists of 4 crucial theorems. The conceptual understanding ofÂ Exercise 4.5 Maths Class 12Â is critical.Â NCERT Solutions for Class 12 Maths Chapter 4Â contains all kinds of different questions from this section of the chapter. Class 12 Exercise 4.5, more or less follows the CBSE exam question pattern. Vedantuâ€™sÂ Class 12 Maths NCERT Solutions Chapter 4 Exercise 4.5Â also follows the same pattern. This helps you get accustomed to the different question types fromÂ Exercise 4.4 Class 12 MathsÂ that can be asked in your board exams. These are step by solutions that have been devised to simplify all complex concepts in simpler terms. They make understanding tough concepts easier.Â
Â Class 12 Maths Chapter 4 comprise of many important topics and subtopics that are essential from your board exam. Here is a list of all topics and subtopics covered in this chapter.
Definition of Determinants
Applications of Determinants
Types of Determinants
First Order Determinant
Second-Order Determinant
Third Order Determinant
Properties of Determinants
Property 1: When the determinantâ€™s columns and rows are interchanged, then the value of the that determinant remains unaffectedÂ
Property 2: The sign of the determinant changes when any two columns or rows of a determinant are interchanged.
Property 3: When any two columns or rows of a determinant are identical, and when the corresponding elements are just the same, then the determinant value is zero.
Property 4: When each element of a column or row of a determinant is multiplied by a constant K then the value also gets multiplied by constant K
Property 5: When some or all elements of a column or row of a determinant are expressed as a sum of two or more terms, then the determinant can be expressed as the sum of two or more determinants.
Property 6: When to each element of any column or row of a determinant, the equimultiples of the corresponding elements of other columns or row are added, then the value of the determinant remains the same i.e., the value of the determinant remains the same if the operation is applied.
Property 7: If each element of column or row is zero then the determinantâ€™s value is zero
Property 8: In a determinant, if all the elements on one side of the principal diagonal are zero, then the value of the determinant is equal to the product of the elements is the principal diagonal.
Area of a Triangle
Minors and Cofactors
Adjoint and Inverse of a Matrix
Theorem 1: When A be any given Square Matrix of order n, then A(adj A)=(adj A)A= AI
Singular and No Singular Matrix
Theorem 2: When A and B are non-singular matrices of the same order, then AB and BA are also non-singular matrices of the same order.
Theorem 3: The determinant of the product of matrices is equal to the product of their respective determinants, that is, AB= |A| |B|, where A and B are Square Matrices of the same order.
Theorem 4: A square matrix A is invertible if and only if A is a non-singular matrix.
Application of Determinants and Matrices
The Solution of a System of Linear Equations Using the Inverse of a Matrix
You should choose Vedantu as your learning hub because it makes learningÂ Class 12 Maths Determinants Exercise 4.5Â and all other exercises interesting, stimulating, though-provoking a happy experience. StudyingÂ Exercise 4.5 Class 12 MathsÂ with Vedantuâ€™s comprehensive NCERT Solutions, LIVE Master Classes and Free Conceptual Videos, LIVE Courses, Lectures, and LIVE Quizzes Online Tests and Ongoing competition will give you a solid hold over the subject matter. It will give you enough practice to perfect your exam preparation. The online tests will help you get well-acquainted with the examination environment an increase your overall speed and efficiency.Â Class 12 Maths Ex. 4.5 SolutionsÂ have been prepared in a strategic manner to help you learn faster and retain for a long period of time.
Vedantu is a prominent digital learning platform. It has a farsighted and futuristic outlook towards learning. It has made astounding efforts towards revolutionizing the learning system of the nation. Through the prudent use of modern technologies, it has dramatically evolved the education space of India. It has made striking efforts towards addressing all the efficacies and discrepancies faced by the current education system. Vedantuâ€™s one of a kind teaching methodologies and state of the art one on one tutorials have made learning a very efficient and productive process. Learning on Vedantu is a more straightforward and natural process. It has transformed the way students perceive learning. It gives you all the personal attention you need and the freedom to study from anywhere. Vedantu is quite the one-stop solution for all your learning related requirements.
1. What does Class 12 Maths Chapter 4 Exercise 4.5 deal with?
Ans: Class 12 Maths Chapter 4 Determinants Exercise 4.5 deals with these topics/ subtopics i.e. 1) Adjoint and Inverse of a Matrix and 2) Adjoint of a matrix. Exercise 4.5 Class 12 Maths consists of 4 crucial theorems. The conceptual understanding of Exercise 4.5 Maths Class 12 is critical. Class 12 Maths Chapter 4 Exercise 4.5 contains all kinds of different questions from this section of the chapter and it follows the CBSE exam question pattern. Thus Vedantuâ€™s Class 12 Maths NCERT Solutions Chapter 4 Exercise 4.5 also follows the same pattern.
This helps you get accustomed to the different question types and its answers/ solutions from Exercise 4.5 that can be asked in the Class 12th board exams. These are step-wise solutions that have been devised to simplify all complex concepts. Thus these make the tough concepts easier.
2. What are the properties of determinants?
Ans: Below are some of the properties of determinants.
Property 1: When the determinantâ€™s columns and rows are interchanged, then the value of that determinant remains unaffectedÂ
Property 2: The sign of the determinant changes when any two columns or rows of a determinant are interchanged.
Property 3: When any two columns or rows of a determinant are identical, and when the corresponding elements are just the same, then the determinant value is zero.
Property 4: When each element of a column or row of a determinant is multiplied by a constant K then the value also gets multiplied by constant K
Property 5: When some or all elements of a column or row of a determinant are expressed as a sum of two or more terms, then the determinant can be expressed as the sum of two or more determinants.
Property 6: When to each element of any column or row of a determinant, the equimultiples of the corresponding elements of other columns or row are added, then the value of the determinant remains the same i.e., the value of the determinant remains the same if the operation is applied.
3. What are theorems discussed in the Class 12 Maths Chapter 4?
Ans: There are a total of four theorems discussed in the Class 12 Maths Chapter 4. They are:
Theorem 1: When A be any given Square Matrix of order n, then A(adj A)=(adj A)A= AI
Theorem 2: When A and B are non-singular matrices of the same order, then AB and BA are also non-singular matrices of the same order.
Theorem 3: The determinant of the product of matrices is equal to the product of their respective determinants, that is, AB= |A| |B|, where A and B are Square Matrices of the same order.
Theorem 4: A square matrix A is invertible if and only if A is a non-singular matrix.
4. How many questions are there in the Class 12 Maths Chapter 4 Exercise 4.5 of NCERT book?
Ans: There are a total of 18 Questions. Out of which, 11 are long-type, five are short-type, and two are multiple-choice questions. We at Vedantu offer the best quality NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.5 which contains solutions/ answers to all these problems/ questions in a concise manner. So that the students of Class 11 can understand the concepts behind all the problems with ease and they can solve those later on their own without any hassle.
Share your contact information
Vedantu academic counsellor will be calling you shortly for your Online Counselling session.