Solve the following system of linear equations using matrices:

$$\begin{gathered} \frac{2}{x}+\frac{3}{y}+\frac{10}{z}=4 \\ \frac{4}{x}-\frac{6}{y}+\frac{5}{z}=1 \\ \frac{6}{x}+\frac{9}{y}-\frac{20}{z}=2 \end{gathered}$$