Linear system/Q/Equivalent over Z/Example/Exercise

1. We consider the linear system over ${}\mathbb {Q}$, consisting of the two equations

   ${}{\frac {3}{7}}x+{\frac {4}{9}}y-{\frac {3}{15}}z={\frac {1}{35}}\,$

   and

   ${}-{\frac {5}{3}}x+{\frac {1}{4}}y-{\frac {6}{7}}z={\frac {11}{10}}\,.$

   Determine a linear system that is equivalent to the given system and has the property that all coefficients are integers.

2. Show that for every system of linear equations over ${}\mathbb {Q}$, there exists an equivalent linear system with the property that all coefficients are integers.

Create a solution