I want to solve these equations using MATLAB and I am sure there is a non zero solution. The equations are:
0.7071*x + 0.7071*z = x -0.5*x +
Friends use MATLAB command rref(A) for Ax=B.... It will give a upper triangular Matrix. Then u can calculate non-trivial solutions easily... But keep in mind that if rref(A)=I (as in your case) then non-trivial solutions do not exist. BEST OF LUCK