I would like to homogenize the size of the elements of the two matrices, but it is impossible for now because there are these fractions. It is really ugly like this.
\documentclass[paper=a4, fontsize=11pt]{scrartcl} \usepackage{amsmath,amsfonts,amsthm,latexsym} \begin{document} \begin{equation} \begin{pmatrix} -\frac{R_a}{L_a} & -\frac{K_g}{L_a} \\ \frac{Ka}{J} & - \frac{f}{J} \end{pmatrix} \begin{pmatrix} i_a(t) \\ \omega(t) \end{pmatrix} \end{equation} \end{document} Here I use TABstacks to build the elements. I control the vertical baselineskip (22pt) and the the horizontal inter-column gap (8pt).
I also created my own \vphantom strut to extend the range of the vector elements.
\documentclass[paper=a4, fontsize=11pt]{scrartcl} \usepackage{amsmath,amsfonts,amsthm,latexsym,tabstackengine} \begin{document} \begin{equation} \setstackgap{L}{22pt} \setstacktabbedgap{8pt} \def\mystrut{\vphantom{\frac{K_g}{J}}} \parenMatrixstack{ -\frac{R_a}{L_a} & -\frac{K_g}{L_a} \\ \frac{Ka}{J} & - \frac{f}{J} } \parenVectorstack{ i_a(t)\mystrut \\ \omega(t)\mystrut } \end{equation} \end{document} 
Another option is to present the result in \displaystyle. Since amsmath is loaded, one can use \dfrac to achieve the result. The "Long" stackgap has been increased to 34pt.
\documentclass[paper=a4, fontsize=11pt]{scrartcl} \usepackage{amsmath,amsfonts,amsthm,latexsym,tabstackengine} \begin{document} \begin{equation} \setstackgap{L}{34pt} \setstacktabbedgap{8pt} \def\mystrut{\vphantom{\dfrac{K_g}{J}}} \parenMatrixstack{ -\dfrac{R_a}{L_a} & -\dfrac{K_g}{L_a} \\ \dfrac{Ka}{J} & - \dfrac{f}{J} } \parenVectorstack{ i_a(t)\mystrut \\ \omega(t)\mystrut } \end{equation} \end{document} 
stackengine package at ctan.org/pkg/stackengine. \displaystyle\frac (or \dfrac if using amsmath). I will revise my answer to demonstrate.