**RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5: **The RD Sharma textbook includes examples before each exercise to help students improve their problem-solving speed. These concepts are described in simple terms, allowing even non-math students to gain a better understanding of the subject. **RD Sharma Class 12 Solutions** are created by a team of experts with the goal of assisting students in their exam preparation. The key topic discussed in this exercise is the solution of a homogeneous system of linear equations. Students can use **RD Sharma Solutions for Class 12 Maths Chapter 6** Determinants Exercise 6.5 to help them succeed in their board exams.

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## Download RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF

RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5

### Access answers to Maths RD Sharma Solutions For Class 12 Chapter 6 – Determinants Exercise 6.5 Important Questions With Solution

**Solve each of the following system of homogeneous linear equations:**

**1. x + y – 2z = 0**

**2x + y – 3z =0**

**5x + 4y – 9z = 0**

**Solution:**

Given x + y – 2z = 0

2x + y – 3z =0

5x + 4y – 9z = 0

Any system of equation can be written in matrix form as AX = B

Now finding the Determinant of these set of equations,

= 1(1 × (– 9) – 4 × (– 3)) – 1(2 × (– 9) – 5 × (– 3)) – 2(4 × 2 – 5 × 1)

= 1(– 9 + 12) – 1(– 18 + 15) – 2(8 – 5)

= 1 × 3 –1 × (– 3) – 2 × 3

= 3 + 3 – 6

= 0

Since D = 0, so the system of equation has infinite solution.

Now let z = k

⇒ x + y = 2k

And 2x + y = 3k

Now using the Cramer’s rule

**2. 2x + 3y + 4z = 0**

**x + y + z = 0**

**2x + 5y – 2z = 0**

**Solution:**

**Chapter 6 Determinants Ex 6.5 Q3****Chapter 6 Determinants Ex 6.5 Q4****Chapter 6 Determinants Ex 6.5 Q5**

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## FAQs on RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5

### What are the advantages of using RD Sharma Solutions for Chapter 6 Exercise 6.5 of Class 12 Maths?

Referring to RD Sharma Solutions for Class 12 Maths Chapter 6 Exercise 6.5 will provide students a good understanding of the type of questions that might be asked in the Class 12 board exam from the chapter.

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### How many questions are there in RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5?

There are a total of 5 questions in RD Sharma Solutions for Class 12 Maths Chapter 6 Exercise 6.5.