TeX Quellcode:

\begin{matrix}\dfrac{5}{6} \vec{t} - 4\vec{s} + \dfrac{7}{2} \vec{q} &=& \dfrac{5}{6} \begin{pmatrix}-27\cr48\cr-38\end{pmatrix} &-& 4\begin{pmatrix}\frac{31}{8}\cr0\cr \frac{1}{12}\end{pmatrix} &+& \dfrac{7}{2} \begin{pmatrix}-44\cr-6\cr \frac{3}{14}\end{pmatrix} \cr \cr &=& \begin{pmatrix}\frac{5}{6} \cdot \left(-27\right)\cr \frac{5}{6} \cdot 48\cr \frac{5}{6} \cdot \left(-38\right)\end{pmatrix} &+& \begin{pmatrix}-4 \cdot \frac{31}{8}\cr-4\cdot 0\cr-4\cdot \frac{1}{12}\end{pmatrix} &+& \begin{pmatrix}\frac{7}{2} \cdot \left(-44\right)\cr \frac{7}{2} \cdot \left(-6\right)\cr \frac{7}{2} \cdot \frac{3}{14}\end{pmatrix} \cr \cr &=& \begin{pmatrix}-\frac{45}{2}\cr40\cr-\frac{95}{3}\end{pmatrix} &+& \begin{pmatrix}-\frac{31}{2}\cr0\cr -\frac{1}{3}\end{pmatrix} &+& \begin{pmatrix}-154\cr-21\cr \frac{3}{4}\end{pmatrix} \cr \cr &=& \begin{pmatrix}-192\cr 19 \cr-\frac{125}{4}\end{pmatrix} \end{matrix}