Text Formatting ⇒ Alignment for Math Expressions in a List

[Sawyier]

I'm a rookie in LaTeX and programming in general, so I'm having quite some trouble. I looked after posts with requests similar to mine, but there just seemed to be a number of different ways of aligning things, so I'm confused on how to do it.

So basically I'm trying to write some mathematical statements:

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1) Assume: a_{1}\vec{v_{1}}+a_{2}\vec{v_{2}}+a_{3}\vec{v_{3}}+...+a_{n}\vec{v_{n}}=\vec{0}, a_{1}\neq 0
\\
2) Write: \vec{v_{1}}+\frac{a_{2}}{a_{1}}\vec{v_{2}}+\frac{a_{3}}{a_{1}}\vec{v_{3}}+...+\frac{a_{n}}{a_{1}}\vec{v_{n}}=\vec{0}
\\\\\\
\vec{v_{1}}=-\frac{a_{2}}{a_{1}}\vec{v_{2}}-\frac{a_{3}}{a_{1}}\vec{v_{3}}-...-\frac{a_{n}}{a_{1}}\vec{v_{n}}

But I'd like the "1) Assume" and "2) Write" to be aligned, like real topics. In addition to that, I'd like to know how to align the two equations I've written for the "2) Write" topic.

Thank you in advance.

[localghost]

For general application of LaTeX you should do some basic reading to learn how to format text. The desired output can be obtained by a list customized by enumitem and advanced math typesetting with amsmath. The below code shows possible approach.

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\documentclass[11pt]{article}
\usepackage[T1]{fontenc}
\usepackage{mathtools}  % loads »amsmath«
\usepackage{enumitem}

\begin{document}
  \begin{enumerate}[label={\arabic*)}]
    \item Assume:
      \(
        a_1\vec{v}_1+a_2\vec{v}_2+a_3\vec{v}_3+\cdots+a_n\vec{v}_n=\vec{0},\ a_{1}\neq 0
      \)
    \item Write:
      \(
        \begin{aligned}[t]
          &\vec{v_{1}}+\frac{a_{2}}{a_{1}}\vec{v_{2}}+\frac{a_{3}}{a_{1}}\vec{v_{3}}+...+\frac{a_{n}}{a_{1}}\vec{v_{n}}=\vec{0} \\
          &\vec{v}_1=-\frac{a_2}{a_1}\vec{v}_2-\frac{a_3}{a_1}\vec{v}_3-\cdots-\frac{a_n}{a_1}\vec{v}_n
        \end{aligned}
      \)
  \end{enumerate}
\end{document}

Further reading:

• The »Math mode« document
• The manuals of the involved packages (see links above).

Best regards and welcome to the board
Thorsten