Extra alignment tab has been changed to \cr. \end{multline}

Question

How do I represent this matrix sum in two lines? I am getting the error "Extra alignment tab has been changed to \cr. \end{multline}"

\begin{multline}
            \begin{bmatrix}
                \dot{i_v} \\ \dot{i_o} \\ \dot{V_o}
            \end{bmatrix} = 
            \begin{bmatrix}
                \frac{-R_f}{L_f} & 0 &\frac{1}{L_f}\\ 0 & \frac{-R_o}{L_o} & \frac{-1}{L_o} \\ \frac{1}{C_f} & \frac{-1}{C_f} & 0
            \end{bmatrix}
            \begin{bmatrix}
                \Delta{i_v} \\ \Delta{i_o} \\ \Delta{V_o}
            \end{bmatrix} +
             \begin{bmatrix}
                \frac{1}{L_f} \\ 0 \\ 0
            \end{bmatrix} 
            \begin{bmatrix}
                \Delta{V_t}
            \end{bmatrix}  
            & + \begin{bmatrix}
                0 \\ \frac{-1}{L_o} \\ 0
            \end{bmatrix} 
            \begin{bmatrix}
                \Delta{V_{dc}}
            \end{bmatrix}
\end{multline}

Answer 1

Your issue sits in

\end{bmatrix}  
& + \begin{bmatrix}

This & is outside the matrices and thus is interpreted by multline. But multline does not support alignments and thus & gives an error here.

You mention in a comment that this is the location where you want a line break. Then replace this & by \\ and you get what you wanted:

\documentclass[a4paper]{article}
\usepackage{amsmath}
\begin{document}
\begin{multline}
  \begin{bmatrix}
    \dot{i_v} \\ \dot{i_o} \\ \dot{V_o}
  \end{bmatrix} = 
  \begin{bmatrix}
    \frac{-R_f}{L_f} & 0 &\frac{1}{L_f}\\ 0 & \frac{-R_o}{L_o} & \frac{-1}{L_o} \\ \frac{1}{C_f} & \frac{-1}{C_f} & 0
  \end{bmatrix}
  \begin{bmatrix}
    \Delta{i_v} \\ \Delta{i_o} \\ \Delta{V_o}
  \end{bmatrix} +
  \begin{bmatrix}
    \frac{1}{L_f} \\ 0 \\ 0
  \end{bmatrix} 
  \begin{bmatrix}
    \Delta{V_t}
  \end{bmatrix}  
  \\
  + \begin{bmatrix}
    0 \\ \frac{-1}{L_o} \\ 0
  \end{bmatrix} 
  \begin{bmatrix}
    \Delta{V_{dc}}
  \end{bmatrix}
\end{multline}
\end{document}