Solve the following system of linear equations using matrix method:

Solve the following system of linear equations using matrix method: $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 9$ $\frac{2}{x} + \frac{5}{y} + \frac{7}{z} = 52$ $\frac{2}{x} + \frac{1}{y} - \frac{1}{z} = 0$