# RS Aggarwal Class 12 Chapter 8 Solutions (System of Linear Equations)

RS Aggarwal Solutions for Class 12 Chapter 8 System of Linear Equations have a crucial role to play if you are appearing in Class 12th board exams. You will get an introduction to the simultaneous linear equations in this chapter along with a step by step explanation of the method of finding the solution of a system of equations. You will also learn consistent and inconsistent systems of equations; and homogeneous and non-homogeneous systems of equations which will only facilitate the process of finding their solutions.

Chapter 8 of RS Aggarwal Solutions consists of only 1 exercise but a wide variety of 23 questions. These exercise solutions ranging from very easy questions to high difficulty level questions will bring you at ease with the topic and help learn time management for the exam which is an important factor to convert your hard work into good marks.

At Instasolv, our objective is to provide an inclusive set of solutions so that you move to the next chapter without any confusions related to the topic. We, at Instasolv, have created these solutions keeping in mind to provide a one-stop solution for all your doubts. By making it a habit of revising these RS Aggarwal Class 12 Solutions, you will easily score good marks in your exams.

## Topics Covered in RS Aggarwal Solutions for Class 12 Chapter 8 **System of Linear Equations**

**Introduction to Simultaneous Linear Equations:**

A system of n simultaneous linear equations in n unknowns x_{1}, x_{2}, x_{3}, …, x_{n} is represented as follows:

a_{11} x_{1} + a_{12} x_{2} + … + a_{1n} x_{n} = b_{1}

a_{21} x_{1} + a_{22} x_{2} + … + a_{1n} x_{n} = b_{2}

… … … … …

… … … … …

a_{n1} x_{1} + a_{n2} x_{n} + … + a_{nn} x_{n} = b_{n}

This system of equations represented in the form of matrices, as follows:

Or, AX = B

Where,

**System of Equations and their Solutions:**

- A set of values of the variable x
_{1}, x_{2}, …, x_{n}satisfying all the equations simultaneously is called a solution of the system. - If a system of equations has one or more solutions, it is called a consistent system of equations, otherwise, it will be known as an inconsistent system of equations.
- If B = O, the system of equations AX = B is called homogeneous. Else, it is known as a non – homogenous system of equations.
- A system AX = B of n linear equations in n equations has a unique solution given by X = A
^{-1}B, if | A | ≠ 0.

If | A | = 0 and (adj A) B =0, then the system is consistent and has an infinite number of solutions.

If | A | = 0 and (adj A) B ≠ 0, then the system has no solution and is inconsistent.

- A homogeneous system of n linear equations in n unknowns can be expressed in the form AX = O.

If | A | ≠ 0, then AX = O has a unique solution X = 0 i.e. x_{1} = x_{2} = … = x_{n} = 0. This solution is called a trivial solution

If | A | = 0, then AX = O has infinite number of solutions

**Algorithm To Find The Solution:**

Step 1: Obtain the system of equations and express it in the matrix equation of the form AX = 0

Step 2: Find | A |.

Step 3: If | A | ≠ 0, then x = y = z = 0 is the only solution of the homogeneous system.

Step 4: If | A | = 0, then the system has infinitely many solutions. In order to find these solutions put z = k and solve any two equations for x and y by matrix method. The values of x and y so obtained with z =k give a solution to the system.

**Important Points to be Remembered **

- You can solve a system of simultaneous linear equations with the help of knowledge about determinants.
- A system of simultaneous equations can be consistent or inconsistent based on their number of solutions.
- When the RHS of the system of simultaneous equations is a null matrix, it is termed as a homogeneous system of equations, else it is called a non-homogeneous system of simultaneous equations.

## Exercise Wise Discussion of RS Aggarwal Solutions for Class 12 Chapter 8 System of Linear Equations

- There is just one exercise 8A in chapter 8, but it provides comprehensive coverage of all the topics employed in your syllabus.
- The exercises have a diverse set of problems fabricated especially to make sure you get to practice the solutions thoroughly.
- These exercise solutions are arranged in an orderly fashion of increasing level of difficulty to match your understanding and groom your analytical skills.
- The exercise in RS Aggarwal Class 12 book will give you an idea about the latest pattern of questions asked in the board exams as well as your competitive exams.
- There are very short answer type questions which are objective in nature and more weightage answers as well, which are subjective in format.
- These solutions will be of great assistance in revision before your school exams.

## Benefits of RS Aggarwal Solutions for Class 12 Maths Chapter 8 by Instasolv

**The answers at Instasolv are easy to understand and are written in easy language for you to clear all your doubts at one place.**- The expert team at Instasolv has prepared these answers after thorough research about the common queries that arise among students.
- The expert tutors of Instasolv are proficient in maths and are committed to giving the easiest way out for the most complex problems in this chapter.