Using align* and array together to show relationship between matrix and system

Question

I am trying to align an entire matrix with a system of equations with an arrow between them. Here is what I have so far,

\begin{align*}
    \left[\begin{array}{ccc|c}
        1 & 0 & 0 & \redtt{b1}  \\
        0 & 1 & 1 & \redtt{b2}  \\
        0 & 0 & 1 & \redtt{b3} 
    \end{array}\right] \longrightarrow && \\
        && x &= \redtt{b1} \\
        && y + z &= \redtt{b2} \\
        && z &= \redtt{b3}
\end{align*}

and it is producing the image below. I would like it to be all inline with itself. Any help would be greatly appreciated. \redtt is just a shortcut I made. It is equivalent to \newcommand{\redtt}[1]{\textcolor{red}{\texttt{#1}}}

Answer 1

Please consider posting complete examples such that others do not have to reverse engineer commands like \redtt. As for your question, you can use aligned or an array.

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{xcolor}
\newcommand{\redtt}[1]{\textcolor{red}{\mathtt{#1}}}
\begin{document}
\begin{align*}
    \left[\begin{array}{ccc|c}
        1 & 0 & 0 & \redtt{b1}  \\
        0 & 1 & 1 & \redtt{b2}  \\
        0 & 0 & 1 & \redtt{b3} 
    \end{array}\right]\quad \longrightarrow\quad \begin{aligned}
        x &= \redtt{b1} \\
        y + z &= \redtt{b2} \\
        z &= \redtt{b3}\\
    \end{aligned} \\
\end{align*}

\begin{align*}
    \left[\begin{array}{ccc|c}
        1 & 0 & 0 & \redtt{b1}  \\
        0 & 1 & 1 & \redtt{b2}  \\
        0 & 0 & 1 & \redtt{b3} 
    \end{array}\right]\quad \longrightarrow\quad \begin{array}{@{}r<{{}}@{}>{{}}l@{}}
        x &= \redtt{b1} \\
        y + z &= \redtt{b2} \\
        z &= \redtt{b3}
    \end{array} \\
\end{align*}
\end{document}

IMHO aligned looks better but in the array you maintain the same spacing between the rows as in the matrix. (Of course one can adjust aligned to give the same spacing, and so on.)

ADDENDUM: As barbara beeton points out, if you only have a one-line equation it is more appropriate to use \[...\].

\documentclass{article}
\usepackage{amsmath}
\usepackage{array}
\usepackage{xcolor}
\newcommand{\redtt}[1]{\textcolor{red}{\mathtt{#1}}}
\begin{document}
\[
    \left[\begin{array}{ccc|c}
        1 & 0 & 0 & \redtt{b1}  \\
        0 & 1 & 1 & \redtt{b2}  \\
        0 & 0 & 1 & \redtt{b3} 
    \end{array}\right]\quad \longrightarrow\quad \begin{aligned}
        x &= \redtt{b1} \\
        y + z &= \redtt{b2} \\
        z &= \redtt{b3}\\
    \end{aligned} 
\]
or
\[
    \left[\begin{array}{ccc|c}
        1 & 0 & 0 & \redtt{b1}  \\
        0 & 1 & 1 & \redtt{b2}  \\
        0 & 0 & 1 & \redtt{b3} 
    \end{array}\right]\quad \longrightarrow\quad \begin{array}{@{}r<{{}}@{}>{{}}l@{}}
        x &= \redtt{b1} \\
        y + z &= \redtt{b2} \\
        z &= \redtt{b3}
    \end{array} \]
\end{document}

Answer 2

I'd simply use a single column array (and avoid pure colors):

\documentclass{article}
\usepackage{amsmath}
\usepackage{xcolor}

\newcommand{\redtt}[1]{\textcolor{red!90!blue}{\mathtt{#1}}}

\begin{document}

\[
\left[\begin{array}{@{}ccc|c@{}}
  1 & 0 & 0 & \redtt{b1}  \\
  0 & 1 & 1 & \redtt{b2}  \\
  0 & 0 & 1 & \redtt{b3} 
\end{array}\right]
\;\longrightarrow\;
\begin{array}{@{}r@{}}
      x = \redtt{b1} \\
  y + z = \redtt{b2} \\
      z = \redtt{b3}
\end{array}
\]

\end{document}