Use thedefinitionof "independence"?

Are there numbers, a, b, c, not all 0, such that

a(1, -1, 2, 3)+ b(2, -1, 1,-1)+ c(-1, 1, 1, 1)= (0, 0, 0, 0)?

If not they are independent. If there are such numbers the vectors are dependent and the equation with those a, b, c is the "dependency relationship".

That is the same as solving the four equations a+ 2b- c= 0, -a- b+ c= 0, 2a+ b+ c= 0, 3a- b+ c= 0. a= b= c= 0 is an obvious solution. Is it the only solution?