2

I'm trying to get this resultenter image description here

However, I'm very new and don't even know where to start with using alignat or making the vertical dots, thank you.

5

Like this?

enter image description here

With use of the directive \vdotswithin{...} from ˙\mathtools` package:

\documentclass{article}
\usepackage{mathtools}

\begin{document}
    \begin{alignat*}{5}
a_{11}x_1 & +{} & a_{12}x_2 +{} & \dotsm              &{} +  a_{1n}x_n & = b_1   \\
a_{21}x_1 & +{} & a_{22}x_2 +{} & \dotsm              &{} +  a_{2n}x_n & = b_2   \\
          &     &               & \vdotswithin{\dotsm}&         \\
a_{m1}x_1 & +{} & a_{m2}x_2 +{} & \dotsm              &{} +  a_{mn}x_n & = b_m
    \end{alignat*}
\end{document}
4

desired equations produced three different ways

Here are three ways to do this:

\documentclass{article}
\usepackage{amsmath}
\begin{document}
    Align, not good, can't get horizontal and vertical dots to line up (easily, could mess around with spacing by eye)
    \begin{align*}
        a_{11}x_1 + a_{12}x_2 + &\dotsb + a_{1n}x_n = b_1\\
        a_{21}x_1 + a_{22}x_2 + &\dotsb + a_{2n}x_n = b_2\\
        &\vdots\\
        a_{m1}x_1 + a_{m2}x_2 + &\dotsb + a_{mn}x_n = b_m
    \end{align*}
    Matrix with two columns, extra spacing around dots
    \[
        \begin{matrix}
            % notice {} before/after & to ensure proper spacing of binary operator (as opposed to the unary version that LaTeX tries to put in if there is no {}
            a_{11}x_1 + a_{12}x_2 + {}&\dotsb&{} + a_{1n}x_n = b_1\\ 
            a_{21}x_1 + a_{22}x_2 + {}&\dotsb&{} + a_{2n}x_n = b_2\\
            & \vdots &\\
            a_{m1}x_1 + a_{m2}x_2 + {}&\dotsb&{} + a_{mn}x_n = b_m
        \end{matrix}
    \]
    Matrix with lots of columns even spacing but larger than in a normal equation.
    Most closely matches example
    \[
            \begin{matrix}
                a_{11}x_1 & + & a_{12}x_2 & + & \dotsb & + & a_{1n}x_n & = & b_1 \\
                a_{21}x_1 & + & a_{22}x_2 & + & \dotsb & + & a_{2n}x_n & = & b_2 \\
                          &   &           &   & \vdots &   &           &   &     \\
                a_{m1}x_1 & + & a_{m2}x_2 & + & \dotsb & + & a_{mn}x_n & = & b_m
        \end{matrix}
    \]
\end{document}

The first uses the align* environment (remove * to have it numbered). This is probably the worst way in my opinon as the vertical dots (\vdots) are not centred on the horizontal dots (\dotsb). The second uses a matrix environment (it does look like these equations come from a matrix after all). There are three columns, one before the dots, one with the dots, and one after the dots. The third uses a matrix environment and each binary operator/relation (+ and =) is in its own column as well as each term and the dots. If I had to guess I'd say this is how the original was done. Notice the large spacing between + and its arguments.

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