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I have just started with algebra and I see here something about homogenous equations but I am just not able to figure it out. I read this answer here,

Homogenous equation in linear algebra?

But still, I couldn't figure it out, what it really means. Here is a photograph of what my book says. If possible please explain it to me! Also i read on google, there is something like non- homogenous equation too. Please explain to me that also.

enter image description here

Thanks a lot!

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  • $\begingroup$ How old is this book ? 1887 ? Can you please tell me the title and author? $\endgroup$ Sep 19, 2016 at 22:27
  • $\begingroup$ @ReneSchipperus Hi! The book's name is "Higher Algebra" by Hall and Knight. And yeah, year was 1887. $\endgroup$ Sep 19, 2016 at 22:36
  • $\begingroup$ And you got it from internet archive ? (a great site !) $\endgroup$ Sep 19, 2016 at 22:38
  • $\begingroup$ Haha, no i actually have a copy of that. I downloaded it so that i can ask questions here on MSE ( by taking screenshots of the pages ) as i have no teacher to explain to me all the stuff that i read. Here's the link to the pdf forgottenbooks.com/en/download/HigherAlgebra_10021865.pdf $\endgroup$ Sep 19, 2016 at 22:48
  • $\begingroup$ Reading such an old book might be a bit hard for a beginner. Personally I like those books, but I first learnt from more modern sources. What is your ultimate goal ? $\endgroup$ Sep 19, 2016 at 22:59

1 Answer 1

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A monomial in several variables has a degree, the sum of all the individual degrees. For example all of the following are degree $3$. $$x^3,y^3,x^2y,xyz.$$

A polynomial is homogeneous if it is a sum of monomials all of the same degree.

The book is saying that if $P(x,y,z)$ is homogenous then say if degree $k$, then $$P(ax,ay,az)=a^kP(x,y,z)$$ So multiplying the variables by a constant $a$ does not change an equation $P(x,y,z)=0$.

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  • $\begingroup$ Thanks for the answer. I will get back to here after I've read it thoroughly . $\endgroup$ Sep 19, 2016 at 22:55

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