RD Sharma Solutions For Class 12 Maths Exercise 8.2 Chapter 8 Solution of Simultaneous Linear Equations

Exercise 8.2 of Chapter 8, Solution of Simultaneous Linear Equations consists of problems on finding the homogeneous system of linear equations. These problems are solved by BYJU’S experts in a simple way to speed up the exam preparation of students. It mainly helps during revision and improves confidence among students before appearing for the board exam. To gain better knowledge about the concepts explained in this exercise, they can refer RD Sharma Solutions Class 12 Maths Chapter 8 Solution of Simultaneous Linear Equations Exercise 8.2 free PDF, which are given below.

RD Sharma Solutions For Class 12 Chapter 8 Solution of Simultaneous Linear Equations Exercise 8.2:-Download PDF Here

RD Sharma Class 12 Maths Solutions Chapter 8 Solutions Of Simultaneous Linear Equations Ex8.2
RD Sharma Class 12 Maths Solutions Chapter 8 Solutions Of Simultaneous Linear Equations Ex8.2 1
RD Sharma Class 12 Maths Solutions Chapter 8 Solutions Of Simultaneous Linear Equations Ex8.2 2
RD Sharma Class 12 Maths Solutions Chapter 8 Solutions Of Simultaneous Linear Equations Ex8.2 3

Access another exercise of RD Sharma Solutions For Class 12 Chapter 8 – Solution of Simultaneous Linear Equations

Exercise 8.1 Solutions

Access answers to Maths RD Sharma Solutions For Class 12 Chapter 8 – Solution of Simultaneous Linear Equations Exercise 8.2

Exercise 8.2 Page No: 8.20

Solve the following systems of homogeneous linear equations by matrix method:

1. 2x – y + z = 0

3x + 2y – z = 0

x + 4y + 3z = 0

Solution:

Given

2x – y + z = 0

3x + 2y – z = 0

X + 4y + 3z = 0

The system can be written as

RD Sharma Solutions for Class 12 Maths Chapter 8 Solutions of Simultaneous Linear Equations Image 115

A X = 0

Now, |A| = 2(6 + 4) + 1(9 + 1) + 1(12 – 2)

|A| = 2(10) + 10 + 10

|A| = 40 ≠ 0

Since, |A|≠ 0, hence x = y = z = 0 is the only solution of this homogeneous equation.

2. 2x – y + 2z = 0
5x + 3y – z = 0
X + 5y – 5z = 0

Solution:

Given 2x – y + 2z = 0

5x + 3y – z = 0

X + 5y – 5z = 0

RD Sharma Solutions for Class 12 Maths Chapter 8 Solutions of Simultaneous Linear Equations Image 116

A X = 0

Now, |A| = 2(– 15 + 5) + 1(– 25 + 1) + 2(25 – 3)

|A| = – 20 – 24 + 44

|A| = 0

Hence, the system has infinite solutions

Let z = k

2x – y = – 2k

5x + 3y = k

RD Sharma Solutions for Class 12 Maths Chapter 8 Solutions of Simultaneous Linear Equations Image 117

3. 3x – y + 2z = 0
4x + 3y + 3z = 0
5x + 7y + 4z = 0

Solution:

Given 3x – y + 2z = 0

4x + 3y + 3z = 0

5x + 7y + 4z = 0

RD Sharma Solutions for Class 12 Maths Chapter 8 Solutions of Simultaneous Linear Equations Image 118

A X = 0

Now, |A| = 3(12 – 21) + 1(16 – 15) + 2(28 – 15)

|A| = – 27 + 1 + 26

|A| = 0

Hence, the system has infinite solutions

Let z = k

3x – y = – 2k

4x + 3y = – 3k

RD Sharma Solutions for Class 12 Maths Chapter 8 Solutions of Simultaneous Linear Equations Image 119

4. x + y – 6z = 0
x – y + 2z = 0
– 3x + y + 2z = 0

Solution:

Given x + y – 6z = 0

x – y + 2z = 0

– 3x + y + 2z = 0

RD Sharma Solutions for Class 12 Maths Chapter 8 Solutions of Simultaneous Linear Equations Image 120

A X = 0

Now, |A| = 1(– 2 – 2) – 1(2 + 6) – 6(1 – 3)

|A| = – 4 – 8 + 12

|A| = 0

Hence, the system has infinite solutions

Let z = k

x + y = 6k

x – y = – 2k

RD Sharma Solutions for Class 12 Maths Chapter 8 Solutions of Simultaneous Linear Equations Image 121

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