Well, thedefinitionof "linear independent" is that no linear combination, au+ bv+ cw, is equal to 0 except for the trivial a= b= c. So look at a(1, 1, 1)+ b(1, m, 1)+ c(1, 1, n)= (0, 0, 0).

That is, of course, equivalent to a+ b+ c= 0, a+ mb+ c= 0, a+ b+ nc= 0. Solve those three equations for a, b, and c. The solution, of course, will depend on m and n. Find values of m and n so that the obvious a= b= c= 0 is NOT the only solution (probably because they make a denominator 0).