Solving a matrices equation with some known answers

a=[3,2,1;
 1,1,0;
 0,1,-1];

b=[x,y,z];
c=a*b;
c=0;

Generally, this matrice equation can be solved easily. However, if one variable is known (e.g. x=1 is known), how can I solve this matrices equation?

What I provided above is a simple case and the actual problem is that an 18x18 coefficient matrix A is known and B is an array that contains 18 variables (x1,x2......x18) in which 10 of the variables are also known, and A*B=0. How can I obtain the rest 8 unknown variables in this matrices equation?

Thank you,

Rick