Školjka

%V0 Consider the sytem of equations $$a_{11}x_1+a_{12}x_2+a_{13}x_3 = 0$$ $$a_{21}x_1+a_{22}x_2+a_{23}x_3 =0$$ $$a_{31}x_1+a_{32}x_2+a_{33}x_3 = 0$$ with unknowns $x_1, x_2, x_3$. The coefficients satisfy the conditions: a) $a_{11}, a_{22}, a_{33}$ are positive numbers; b) the remaining coefficients are negative numbers; c) in each equation, the sum ofthe coefficients is positive. Prove that the given system has only the solution $x_1=x_2=x_3=0$.