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.
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
We have provided complete details of RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5. If you have any queries related to CBSE Class 12 Exam, feel free to ask us in the comment section below.
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.
Where can I get RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF?
You can get RD Sharma Solutions Class 12 Maths Chapter 6 Exercise 6.5 Free PDF from the above article.
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.