  The multiple zeta values (MZV) are a set of real numbers with a beautiful
structure as an algebra over the rational numbers. They are related to maybe
the most important conjecture on mathematics today, the Riemann hypothesis. In
this paper we will show partial solutions to five well known conjectures about
the MZV which we partially proved using just linear systems and shuffles
products. We saw that to partially solve four of this conjectures we only need
linear algebra.
