Matrix environments not being typeset

Question

Why does LaTeX seem to have a problem with the matrix environment, and why does it tell me something about \hbox badness 10000?

\documentclass[12pt,fleqn]{article}
\usepackage[utf8]{inputenc}
\usepackage{mathtools}
\usepackage{amsfonts}
\usepackage{amssymb}
\author{karl}
\begin{document}
6) \\
\begin{eqnarray} 
a_1=a_1*b_1& \\
a_2=a_1*b_2&+a_2*b_3\\
a_3=a_3*b_3&
\end{eqnarray} 
\begin{matrix}
1 \\ 
0 \\ 
1
\end{matrix}
\begin{eqnarray}
b_1=a_1*b_1& \\
b_2=a_1*b_2&+a_2*b_3\\
b_3=a_3*b_3&
\end{eqnarray}
bei festem b liefert Koefizientenvergleich für a die Triviallösung
\begin{matrix}
 1 \\ 
 0 \\ 
 1
\end{matrix}
Somit gibt es für beide Seiten das gleiche Element was auf der Identität abbildet, somit ist
\begin{matrix}
 1 \\ 
 0 \\ 
 1
\end{matrix}
 auch das neutrale Element \\
\end{document}

Answer 1

The matrix environments need to be placed in math mode. For that, either use $\begin{matrix}...\end{matrix}$, or \[\begin{matrix}...\end{matrix}\]. The former is an in-line math expression, while the latter is a display math environment.

The \hbox badness stems from lines that are too wide to fit within the text block margins, or when you're using inappropriate line-breaking techniques. The latter case occurs when you issue

6) \\
<more stuff>

It's better to remove the \\ and leave a blank line between the content. This will be similar to a regular paragraph break. If you plan on enumerating content, consider using an enumerate list.

Other suggestions:

• Use \times instead of * to represent multiplication (or drop it altogether, since it makes sense within a mathematical context); and
• Use align-and-friends instead of eqnarray (see eqnarray vs align)