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

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Why are systems of linear equations of the form Ax=0 called homogeneous?    What is the motivation behind the word &quot;homogeneous&quot;?

ImpudgeIntemnect · Accepted Answer

Because in the equation    A11x1+⋯+A1nxn=0    A11x1+⋯+A1nxn=0    all terms are of degree 1. On the other hand, the equation Ax=b also has terms of degree 0.

Mikayla Swan · Accepted Answer

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.

Why are systems of linear equations of the form Ax=0 called homogeneous? What is the...

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