Understanding Homogeneous Systems - Expert Answers and Guidance

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In summary, a homogeneous system is a set of equations where all the variables have the same degree. To solve it, one must use the substitution method by isolating and substituting variables until all are solved for. Understanding homogeneous systems is important as they are widely used in science, engineering, and other fields. A homogeneous system can have multiple solutions, making it underdetermined. Real-life applications of these systems include physics, chemistry, economics, and computer science.
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manal950
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Hi all

I have question in homogeneous .

893204297.jpg


could please check my answer ?
 
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You have a serious error right at the start. You have, on the right, [itex](x+ y)^2[/itex] and you divide that by [itex]x^2[/itex] to get [itex](1+ y/x)^2= (1+ v)^2[/itex]

Up to there you are correct. But then your next line has [itex]1+ v^2[/itex] which is NOT the same thing. [tex](1+ v^2)= 1+ 2v+ v^2[/tex] which works nicely in canceling that "-2v" you will introduce.
 

1. What is a homogeneous system?

A homogeneous system is a set of equations where all the variables have the same degree. In other words, the equations all have the same number of variables with the same powers.

2. How do you solve a homogeneous system?

To solve a homogeneous system, you must use a method called substitution. This involves isolating one variable in one of the equations and substituting it into another equation. Continue this process until all the variables are isolated and then solve for each variable.

3. What is the importance of understanding homogeneous systems?

Understanding homogeneous systems is important because they are used in many areas of science and engineering to model and solve complex systems. They also provide a foundation for understanding more advanced mathematical concepts.

4. Can a homogeneous system have multiple solutions?

Yes, a homogeneous system can have infinitely many solutions. This is because when all the variables have the same degree, the system becomes underdetermined and has an infinite number of possible solutions.

5. What are some real-life applications of homogeneous systems?

Homogeneous systems are used in many real-life applications, such as in physics to model the motion of objects, in chemistry to represent chemical reactions, and in economics to analyze supply and demand. They are also used in computer science for image and signal processing.

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