How can I make all of the columns in my aligned environment left-aligned?

Question

I am trying to produce a three line equation, aligned on the start of each line and on the plus signs. I have tried this

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{aligned}
     &1\cdot \varepsilon_1&+ 1\cdot \varepsilon_2 &+ \dots + 1\cdot \varepsilon_n\
     &X_{21} \cdot \varepsilon_1 &+ X_{22} \cdot \varepsilon_2 &+ \dots + X_{2n} \cdot \varepsilon_n\
     &X_{k1} \cdot \varepsilon_1 &+ X_{k 2} \cdot \varepsilon_2 &+ \dots + X_{kn} \cdot \varepsilon_n \
\end{aligned}
\end{equation}
\end{document}

Which produces this

I tried replacing the 1's in the first line with X_{21}, X_{22} etc as in the second line, and it aligns properly then, but when I use 1's again, the equations go back to being unaligned again.

Answer 1

Remember 2n-1 &'s on each line with n alignments. n &'s for alignments and n-1 &'s to separate the alignment columns. I'd also use alignedat instead as in this example

\documentclass[a4paper]{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{alignedat}{3}
     &1\cdot \varepsilon_1 &&+ 1\cdot \varepsilon_2 &&+ \dots + 1\cdot \varepsilon_n\
     &X_{21} \cdot \varepsilon_1 &&+ X_{22} \cdot \varepsilon_2 &&+ \dots + X_{2n} \cdot \varepsilon_n\
     &X_{k1} \cdot \varepsilon_1 &&+ X_{k 2} \cdot \varepsilon_2 &&+ \dots + X_{kn} \cdot \varepsilon_n \
\end{alignedat}
\end{equation}
\end{document}

Answer 2

Here are three more array-based solutions. One each depending on whether the cell contents should be left-aligned, centered, or right-aligned. Observe that contents of the three array environments are identical; they only differ in the use of the L, C, and R column types.

A separate topic: The code uses \cdots rather than \dots, as LaTeX doesn't "know" that the dots will be flanked by + (a binary operator) on either side -- but in the adjacent cells.( If +\dots+ is found, LaTeX is smart enough to change \dots to \cdots.)

\documentclass{article} % or some other suitable document class
\usepackage{array} % for '\newcolumntype' macro
\newcolumntype{O}{>{{}}c<{{}}} % for operators ( + , \cdot )
\newcolumntype{C}{>{\displaystyle}c}
\newcolumntype{L}{>{\displaystyle}l}
\newcolumntype{R}{>{\displaystyle}r}
\usepackage{amsmath} % for 'gather' environment
\begin{document}
\setlength\arraycolsep{0pt}
\renewcommand\arraystretch{1.33}
\begin{gather}
\begin{array}{ {6}{LO} L }  % left-aligned
1      &\cdot& \varepsilon_1 &+& 1       &\cdot& \varepsilon_2 &+& \cdots &+& 1      &\cdot& \varepsilon_n\
X_{21} &\cdot& \varepsilon_1 &+& X_{22}  &\cdot& \varepsilon_2 &+& \cdots &+& X_{2n} &\cdot& \varepsilon_n\
X_{k1} &\cdot& \varepsilon_1 &+& X_{k 2} &\cdot& \varepsilon_2 &+& \cdots &+& X_{kn} &\cdot& \varepsilon_n
\end{array} 
\[2\jot]
\begin{array}{ {6}{CO} C }  % centered
1      &\cdot& \varepsilon_1 &+& 1       &\cdot& \varepsilon_2 &+& \cdots &+& 1      &\cdot& \varepsilon_n\
X_{21} &\cdot& \varepsilon_1 &+& X_{22}  &\cdot& \varepsilon_2 &+& \cdots &+& X_{2n} &\cdot& \varepsilon_n\
X_{k1} &\cdot& \varepsilon_1 &+& X_{k 2} &\cdot& \varepsilon_2 &+& \cdots &+& X_{kn} &\cdot& \varepsilon_n
\end{array} 
\[2\jot]
\begin{array}{ *{6}{RO} R }  % right-aligned
1      &\cdot& \varepsilon_1 &+& 1       &\cdot& \varepsilon_2 &+& \cdots &+& 1      &\cdot& \varepsilon_n\
X_{21} &\cdot& \varepsilon_1 &+& X_{22}  &\cdot& \varepsilon_2 &+& \cdots &+& X_{2n} &\cdot& \varepsilon_n\
X_{k1} &\cdot& \varepsilon_1 &+& X_{k 2} &\cdot& \varepsilon_2 &+& \cdots &+& X_{kn} &\cdot& \varepsilon_n
\end{array}
\end{gather}
\end{document}