# RS Aggarwal Class 12 Solutions Chapter 7

## RS Aggarwal Solutions Class 12 Chapter 7 Adjoint and Inverse of a Matrix Solutions PDF Download

#### RS Aggarwal Solutions Class 12 Maths Chapterwise â€“ Free PDF Download

We’ve put together RS Aggarwal Class 12 Solutions Chapter 7 Adjoint and Inverse of a Matrix to help you understand the important questions. From the point of view of the RS Aggarwal Solutions for Class 12 Board exam, this is a very important chapter. You will learn how to use equations and simple operations to find the adjoint of a given matrix and the inverse of any matrix. Exercise solutions will also talk about the properties of the inverse of matrices.

When students have completed RS Aggarwal class 12 adjoint and the Inverse of a matrix, they will know how to find the matrix’s transpose and its Inverse. It will also teach students how to use different operations on the columns of a matrix and when to do so.

This chapter has 37 questions and one exercise that will give you a chance to practise a lot of different things. By looking at these solutions, you’ll learn how to make the most of your time and avoid making silly mistakes. For each exercise question, a clear answer is given that explains all the operations. This is done to avoid the general confusion that often happens when finding the adjoint and inverse of a matrix. These questions will help you learn matrices well, which is important not only for college but also for your CBSE Board Exams.

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**RS Aggawal Class 12 Solutions Chapter 7 free PDF Download**

**RS Aggawal Class 12 Solutions Chapter 7 free PDF Download**

**RS Aggarwal Class 12 Solutions**

## Chapter-1 Relation Solutions

## Chapter-2 Functions Solutions

## Chapter-3 Binary Operations Solutions

## Chapter-4 Inverse Trigonometric Functions Solutions

## Chapter-5 Matrices Solutions

## Chapter-6 Determinants Solutions

## Chapter-7 Adjoint and Inverse of a Matrix Solutions

## Chapter-8 System of Linear Equations Solutions

## Chapter-9 Continuity and Differentiability Solutions

## Chapter-10 Differentiation Solutions

## Chapter-11 Applications of Derivatives Solutions

## Chapter-12 Indefinite Integral Solutions

## Chapter-13 Method of Integration Solutions

## Chapter-14 Some Special Integrals Solutions

## Chapter-15 Integration Using Partial Fractions Solutions

## Chapter-16 Definite Integrals Solutions

## Chapter-17 Area of Bounded Regions Solutions

## Chapter-18 Differential Equations and Their Formation Solutions

## Chapter-19 Differential Equations with Variable Separable Solutions

## Chapter-20 Homogeneous Differential Equations Solutions

## Chapter-21 Linear Differential Equations Solutions

## Chapter-22 Vectors and Their Properties Solutions

## Chapter-23 Scalar, or Dot, Product of Vectors Solutions

## Chapter-24 Cross, or Vector, Product of Vectors Solutions

## Chapter-25 Product of Three Vectors Solutions

## Chapter-26 Fundamental Concepts of 3-Dimensional Geometry Solutions

## Chapter-27 Straight Line in Space Solutions

## Chapter-28 The Plane Solutions

## Chapter-29 Probability Solutions

## Chapter-30 Bayesâ€™s Theorem and its Applications Solutions

## Chapter-31 Probability Distribution Solutions

## Chapter-32 Binomial Distribution Solutions

## Chapter-33 Linear Programming Solutions

#### RS Aggarwal Class 12 Solutions Chapter 7 Free PDF Download

You can find the answers to each question in the RS Aggarwal Class 12 Solutions chapter 7 , which are in the back of your RS Aggarwal textbook. Students will learn to solve both short and long five-mark questions. They will learn to multiply the elements in the matrix and invert the matrix to see if it proves the invertible symmetric matrix rule.

So, learning becomes about new ideas, and it will be much easier to use the formula to solve problems related to adjoints. People say that RS Aggarwal questions are some of the hardest to solve, which is why we made our own solution PDF.

##### Detail Highlights of RS Aggarwal Class 12 Solutions Chapter 7 “Adjoint and Inverse of a Matrix”

- The adjoint of a matrix A is the transpose of the matrix of cofactors of all the elements in A. It is written as adj A.
- If AB = In = BA, then the inverse of A would be A-1 = B.
- We can use either of the two operations, A = IA or I = BA, to find the inverse.

##### Discussion about RS Aggarwal Solutions for Class 12 Chapter 7 for Adjoint and Inverse of a Matrix Exercise

- There is one exercise 7A that goes over all of this chapter’s topics in depth.
- You will need to find the adjoint and inverse of the matrices.
- Some questions will also ask you to use what you know about the properties of a matrix’s inverse.
- There are questions with short answers that are based on facts and questions with long answers that are based on opinions.
- The questions are in order of how hard they are, so you can see if you know enough about the topics.
- You will get an idea of how the questions on your test will be set up.

##### Advantages of RS Aggarwal Class 12 Solutions Chapter 7 by Utopper

- The answers that the team at Utopper gives are written in the simplest way possible so that you can get good grades.
- The exercise solutions that Utopper has put together are easy to find and don’t cost anything.
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- These RS Aggarwal Class 12 Solutions Chapter 7 Solutions will help you make the most of the time you have to study before your test.
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- The solutions are very reliable because they are based on the strict rules of the Class 12 CBSE Board.

## FAQ ( Frequently Asked Questions )

**1. What is Adjoints?**

Ans – The cofactor matrix of a given matrix is said to be the adjoint of that matrix. Any matrix that can be written as (A) also has an adjoint, which is written as adj (A). Also, if you multiply the matrix by its inverse, you will get A-1, which is the identity matrix. You could even say that an identity matrix is a unit matrix where both the matrix A and its inverse are (n x m) square matrices with ones on one diagonal and zeros everywhere else.

**2. What are the different kinds of matrics?**

Ans – There are six different kinds of matrices: square, symmetric, triangular, diagonal, identity, and orthogonal. From these six matrices, only a few are used often. These are Square matrices, which means that the number of rows and columns are the same. On the other hand, a rectangular matrix is one that doesn’t have the same number of rows and columns.

In the same way, the symmetric matrix is also a square, but the triangles in the top right and bottom left corners are the same. The diagonal matrix is one in which all of the values outside of the main diagonal have zero, and the main diagonal goes from the top left to the bottom right. Last, there’s an identity matrix, whose vectors don’t change when you multiply them.

**3. What are the different theorems that RS Aggarwal Class 12 Solutions Chapter 7 explains?**

Ans – In RS Aggarwal Class 12 Solutions Chapter 7 tells the students about four different theorems. These theorems help the students understand the main ideas of the chapter better. Here is a list of the four theorems:

- First theorem: If A is any n-by-n square matrix, then A (Adj A) is the same as (Adj A) A, which is the same as A I, where I is the n-by-n identity matrix.
- Theorem 2: If A and B are both non-singular matrices of the same order, then AB and BA are also of the same order.
- Theorem 3: If A and B are both square matrices of the same order, then the determinant of their product is equal to the product of their determinants, i.e., IAI IBI = AB
- Theorem 4: If A is not singular, then A is also a square matrix that can be turned into a singular matrix.

**4. How do I study for my board exams for Class 12 Chapter 7?**

Ans – Students in class 12 have to work hard to do well on the board exams with help of utopper Study materials like previous year papers, sample papers, important questions. Not only do they have to study for the board exams, but they also have to prepare for the competitive exams. Because of this, it is important to get a good grasp of the ideas. Students can study for class 12 chapter 7 with the help of the RS Aggarwal Class 12 Solutions Chapter 7 on Utopper.