Clu Linear Algebra Ch 1 Questions

This is an example of a question with reasonable syntax. The system can be improved, but this should work as a first pass at one.

Mickey: I'm not sure I understand the difference between Homogeneous and non-Homogeneous equations. Is there anyone who can help?

Mickey: Well, a homogeneous equation is one that equals zero while a non-homogeneous equation equals something else. For instance,

(1)
\begin{matrix} 1 & 0 & 0 & | & 0 \\ 0 & 1 & 0 & | & 0 \\ 0 & 0 & 1 & | & 0 \\ \end{matrix}

is homogeneous because each equation $x_1(\vec{a}) + x_2(\vec{b}) + x_3(\vec{c}) = \vec{0}$. If it equaled anything else, it would be considered non-homogeneous. Similarly, this matrix is considered linearly independent because there is no solution that is non-trivial (non-zero).

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