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"?

What is the motivation behind the word "homogeneous"?

ImpudgeIntemnect

Beginner2022-02-19Added 6 answers

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.

all terms are of degree 1. On the other hand, the equation

Mikayla Swan

Beginner2022-02-20Added 9 answers

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.

So homogeneity refers to the fact that all therms have the same degree.