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.
Thanks a lot!
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 $P(x,y,z)=0$.