MATLAB Solving equations problem

Question

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 +         


        

Answer 1

A = [ 0.7071 0 0.7071 ;
      -0.5 0.7071 0.5 ;
    -0.5 -0.7071 0.5 ];
B = [1 ; 1 ; 1];

AA = A-diag(B)

      -0.2929            0       0.7071
         -0.5      -0.2929          0.5
         -0.5      -0.7071         -0.5

BB = B-B

     0
     0
     0

AA\BB

     0
     0
     0