Finding solutions to a vector equation?!?!
I have the question: find all solutions (x1,x2,x3) to the vector equation x1v1 + x2v2 + x3v3 = 0 when :
a) v1 = (1,1,1), v2 = (1,0,1), v3 = (1,1,2)?
b) v1 = (1,1,-1), v2 = (1,1,-3), v3 = (-1,-1,1)?
For a) I row reduced it to x1 = 0, x2 = 0, x3 = 0, but this seemed to be a trivial solution. For b) it row reduced to x1 = x3 and x2 = 0. I am not sure if this is correct.
Could someone please help?