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 of Exercise 4.5 Maths Class 12 is critical. NCERT Solutions for Class 12 Maths Chapter 4 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. Vedantu’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 from Exercise 4.4 Class 12 Maths 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.
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
Third Order Determinant
Properties of Determinants
Property 1: When the determinant’s columns and rows are interchanged, then the value of the that determinant remains unaffected
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 determinant’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
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