# RS Aggarwal Class 12 Chapter 6 Solutions (Determinants)

RS Aggarwal Solutions for Class 12 Chapter 6 Determinants** **have been prepared to help you solve the difficult questions easily. You will be introduced to Determinants in this chapter and also learn how to find the determinant of square matrices of orders 1, 2 and 3 respectively. You will also be introduced to some interesting properties of determinants of square matrices. You will find that it is very simple to find the values of determinants with the application of these new properties, which would have been a complicated task otherwise.

This chapter consists of 4 exercises containing a sum total of 110 questions, with thorough coverage of all the important topics given in the syllabus prescribed by the CBSE. This is one of the most scoring chapters in Class 12 syllabus, therefore you should practice all the questions discussed in the RS Aggarwal Solutions for Class 12 Chapter 6** **thoroughly to achieve a spike in your marks in Maths. The questions are in an increasing level of difficulty so that you are able to adjust with the new concepts immediately.

The team of Subject Matter Experts at Instasolv are aware of your requirements for the simplicity of language and thus have adhered to the requirements for the Class 12 board exams. We, at Instasolv, follow strict guidelines in various stages of creating the answers, clearing all your doubts and concepts at one place in a hustle-free format.

## Summary of RS Aggarwal Solutions for Class 12 Chapter 6 Determinants

**Introduction to Determinants:**

Any square matrix can be represented as an expression or a numeric digit. This is known as its determinant. For any square matrix A_{nxn,}, its determinant can be denoted by det A or | A |.

**Determinant:**

**The determinant of a Square Matrix of Order 1:**

For the matrix A = [a], | A | = a

**The determinant of a Square Matrix of Order 2:**

For a square matrix of order 2, the determinant can found by subtracting the product of the elements of the main diagonal and the product of the elements of the counter-diagonal.

**The determinant of a Square Matrix of Order 3:**

For a square matrix of order 2, the determinant can found by representing the matrix in the form of second-order determinants. This method is called the expansion of determinant. It can either be done along a row or column.

Expanding along R1 –

| A | = a_{11} (a_{22} a_{33} – a_{32} a_{23}) – a_{12} (a_{21} a_{33} – a_{31} a_{23}) + a_{13} (a_{21} a_{32} – a_{31} a_{22}

OR

Expanding along C_{1}–

| A | = a_{11} (a_{22} a_{33} – a_{23} a_{32}) – a_{21} (a_{12} a_{33} – a_{13} a_{32}) + a_{31} (a_{12} a_{23} – a_{13} a_{22}

**Properties of Determinants:**

Property 1: Rows and columns can be interchanged without affecting the value of the determinant.

Property 2: Interchanging of rows or columns changes the sign of the determinant.

Property 3: The value of a determinant is zero if identical rows or columns are present

Property 4: If a row or a column is multiplied by any constant say k, the value of determinant also becomes k times

Property 5: If a row or a column of a determinant can be represented as a sum of

more than one term, the determinant can be represented as a sum of more than one determinant.

Property 6: If we will add the equimultiples of all rows or all columns of a determinant to the corresponding elements of another row or column respectively, then the value of the determinant will not change.

**Area of Triangle:**

The area of a triangle represented by the given 3 locus points (x_{1},y_{1})(x_{3},y_{3})(x_{3},y_{3})can be calculated by the following formula:

This formula can be represented in the form of determinants as follows:

**Highlights of the Chapter:**

- Representation of a square matrix in the form of a numerical digit or an expression is known as a determinant.
- We can find the area of a triangle using determinants with the help of the following formula:

- There are various properties of determinants with the help of which you can easily determine the numerical value of a given matrix.
- You can find the determinant of a matrix by learning to practice its expansion in a 3X3 matrix using the following formula:

Expanding along R1 –

| A | = a_{11} (a_{22} a_{33} – a_{32} a_{23}) – a_{12} (a_{21} a_{33} – a_{31} a_{23}) + a_{13} (a_{21} a_{32} – a_{31} a_{22})

OR

Expanding along C1 –

| A | = a_{11} (a_{22} a_{33} – a_{23} a_{32}) – a_{21} (a_{12} a_{33} – a_{13} a_{32}) + a_{31} (a_{12} a_{23} – a_{13} a_{22})

## Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 6 ‘Determinants’

- The exercise solutions of 6A consist of advanced level short answer type questions, to evaluate the value of a given determinant or to find the value of an unknown variable, merely by the expansion of the matrix.
- In exercise 6B, you will learn the application of the important properties and will be able to prove various equations and theorems using them besides practising the evaluation of complex determinants.
- You will be required to find the area of triangles or prove collinearity of three points using determinants in the last exercise 6D.
- Solving these questions will train you extensively in your time management skills and boost your analytical skills.

## Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 6 by Instasolv

- The complicated RS Arrarwal Class 12 Maths Solutions are mentioned in the simplest manner possible by the maths experts at Instasolv.
- We have covered each question of each exercise to cater to your needs of improving your ability to approach a problem of determinants.
- The answers provided at Instasolv are free and easily accessible so that you can sort out all your queries at one place.