Problem #PRU-78130

Problems Set theory and logic Theory of algotithms Game theory Game theory (other) Algebra Algebraic equations and systems of equations Systems of linear equations
 12–14  3.0

Problem

There is a system of equations \[\begin{aligned} * x + * y + * z &= 0,\\ * x + * y + * z &= 0,\\ * x + * y + * z &= 0. \end{aligned}\] Two people alternately enter a number instead of a star. Prove that the player that goes first can always ensure that the system has a non-zero solution.