Is x = <1,2,-1> a linear combination of u1 = <1,1,1>, u2 = <1,1,0> and u3 = <1,0,-1>? If so, find the linear combination.
If it is, then there must exist numbers a, b, c so that <1, 2, -1>= a<1, 1, 1>+ b<1, 1, 0>+ c<1, 0, -1>= <a, a, a>+ <b, b, 0>+ <c, 0, -c>= <a+ b+ c,a+ b, a- c>. In order for that to be true, we must have a+ b+ c= 1, a+ b= 2, and a- c= -1. Can you solve those three equations?