a--
A={{2,1,1},{-2,1,2},{2,3,-4}};
b={6,1,3};
LinearSolve[A,b]
s+ i
b ---
A={{2,1,1},{-2,1,2},{2,3,-4}};
b={6,1,3};
d=Inverse[A];
d.b
s+i
c----,
A={{2,1,1},{-2,1,2},{2,3,-4}};
A1={{6,1,1},{1,1,2},{3,3,-4}};
A2={{2,6,1},{-2,1,2},{2,3,-4}};
A3={{2,1,6},{-2,1,2},{2,3,3}};
{Det[A1]/Det[A],Det[A2]/Det[A],Det[A3]/Det[A]}