Numbers with a minus sign in a matrix not aligned with the numbers without minus sign

Question

What should I do to get all the 1 with a minus sign (-) in front of them aligned with the other 1 and the 0 in those vectors?

\documentclass[a4paper, 12pt]{book}
\usepackage{amsmath}
\begin{document}
$$
v_1 = \begin{bmatrix} 1 \\ -1 \\ 0 \\0 \end{bmatrix}, \quad
v_2 = \begin{bmatrix} 1 \\ 0 \\ -1 \\0 \end{bmatrix}, \quad
v_3 = \begin{bmatrix} 1 \\ 0 \\ 0 \\-1 \end{bmatrix},
$$
\end{document}

Answer 1

As you've discovered, the bmatrix environment centers the cell contents. To achieve right-alignment, you may want to load the mathtools package (a superset of the amsmath package) and use a bmatrix* environment with optional argument r.

\documentclass[a4paper, 12pt]{book}
\usepackage{mathtools}
\begin{document}
\[
v_1 = \begin{bmatrix} 1 \\ -1 \\ 0 \\0 \end{bmatrix}, \quad
v_2 = \begin{bmatrix} 1 \\ 0 \\ -1 \\0 \end{bmatrix}, \quad
v_3 = \begin{bmatrix} 1 \\ 0 \\ 0 \\-1 \end{bmatrix}.
\]

\[
v_1 = \begin{bmatrix*}[r] 1 \\ -1 \\ 0 \\0 \end{bmatrix*}, \quad
v_2 = \begin{bmatrix*}[r] 1 \\ 0 \\ -1 \\0 \end{bmatrix*}, \quad
v_3 = \begin{bmatrix*}[r] 1 \\ 0 \\ 0 \\-1 \end{bmatrix*}.
\]
\end{document}