# RD Sharma Class 12 Chapter 6 Solutions (Determinants)

RD Sharma Class 12 Maths Solutions for Chapter 6 ‘Determinants’ cannot be ignored from the CBSE exam point of view. To be able to grasp the concepts of this chapter of RD Sharma Class 12 Solutions, it is very important to get through with the previous chapter as the problems in this chapter involves the operation of matrices. This chapter has 114 questions in 5 exercises. There is the involvement of concepts like the expansion of determinants, minors and cofactors, adjoint of a matrix, etc.

The solutions offered in the RD Sharma Class 12 Maths Solutions Chapter 6 at the Instasolv experts are simpler and also include the methodical explanation of all problems of the chapter. Our experts have created these solutions for you help at times when you are unable to understand a particular problem or concept of the chapter. We ensure that you will see a rise in your class performance as you will refer to our RD Sharma solutions for studying.

## Important Topics of RD Sharma Class 12 Maths Chapter 6 – Determinants

**What is a Determinant?**

Let us suppose there is a square matrix M. Now, we know from the knowledge of the previous chapter that a square matrix is a matrix with an equal number of rows and columns. Now let us suppose there are ‘a’ number of terms in that square matrix. So, the determinant is the sum of all the ‘a’ terms in the matrix. It is also denoted by |M|.

**Area of a Triangle **Let us consider a triangle. The vertices of the triangle are given by the coordinates (a, p), (b, q) and (c, r), is given by the expression,

Area = ½ [a(q–r) + b (r–p) + c(p–q)].

So, the above formula can also be written as follows:-

**Minors and Cofactors **

Suppose there is a determinant with x rows and y columns. So, what we do is that we delete the extreme most row and column of the determinant and then minor we formed as illustrated below:

E.g.: Find the minor of the element 6 in the determinant ∆ =

Solution: Since 6 lies in the second row and third column, its minor M23 given by,

( obtained by deleting R2 and C3 in ∆ )

The other concepts that have been taught are below:-

- Expansion of Determinants
- Properties of Determinants
- Minors and Cofactors
- Area of Triangles
- Adjoint and Inverse of a Matrix
- Application of Determinant and Matrix

## Exercise Discussion for RD Sharma Class 12 Maths Chapter 6 – Determinants

- Exercise 6.1 deals with the problems on expansion, minors and cofactors etc. and has 12 questions in it.
- Exercise 6.2 is the biggest exercise which mostly includes problems of the type “prove that…”. These problems are based on the properties of determinants and have 52 questions.
- Exercise 6.3 has 13 problems on finding areas of triangles using the determinants.
- Exercise 6.4 includes the problems of solving linear equations using the determinants. There are 32 questions with 4 basic types.
- The last exercise is 6.5 and it contains 5 questions which are helpful in analysing your knowledge on determinants.

## Benefits of RD Sharma Class 12 Maths Chapter 6 – Determinants by Instasolv

The RD Sharma Solutions that are provided by Instasolv are very lucid and easy to understand. The experts at Instasolv devise the solutions that provide you with a stepwise guide which is crucial to gain marks and momentum for CBSE board exam. Our RD Sharma Class 12 Maths Solutions are the apt study guides for you to refer to.