\documentclass[../script.tex]{subfiles}

% !TEX root = ../../script.tex

\begin{document}
    \chapter{Linear Algebra} 
    \vspace*{\fill}\par
    \pagebreak  

    \subfile{sections/vector_spaces.tex}
    \subfile{sections/matrices.tex}
    \subfile{sections/determinant.tex}
    \subfile{sections/scalar_product.tex}
    \subfile{sections/eigenvalue.tex}
\end{document}