 # NCERT Solutions for Class 12 Maths Chapter 4- Determinants Exercise 4.5  View Notes

## NCERT Solutions for Class 12 Maths Chapter 4- Determinants Exercise 4.5

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.  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.

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 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 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 determinant’s columns and rows are interchanged, then the value of 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.

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.

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