\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
    \begin{bmatrix}P_z \\ P_y \\ P_x \\ 1\end{bmatrix}
    =
    \begin{bmatrix}
        k_3 & Y_z \Delta r & X_z \Delta c & S_z \\
        k_2 & Y_y \Delta r & X_y \Delta c & S_y \\
        k_1 & Y_x \Delta r & X_x \Delta c & S_x \\
          0 &      0 &      0 &  1
    \end{bmatrix}
    \begin{bmatrix}s \\ r \\ c \\ 1\end{bmatrix}
\end{equation}
\end{document}
