lovesickgirlsrd5

2022-02-18

Why are systems of linear equations of the form $Ax=0$ called homogeneous?
What is the motivation behind the word "homogeneous"?

ImpudgeIntemnect

Because in the equation
${A}_{11}{x}_{1}+\cdots +{A}_{1n}{x}_{n}=0$
${A}_{11}{x}_{1}+\cdots +{A}_{1n}{x}_{n}=0$
all terms are of degree 1. On the other hand, the equation $Ax=b$ also has terms of degree 0.

Mikayla Swan

A system of equation is linear if any equation is first degree and is homogeneous if any term (not null) in any equation has the same degree.
So homogeneity refers to the fact that all therms have the same degree.

Do you have a similar question?