(** SISTEMI LINEARI **)

(* PRIMO SISTEMA *)

a={{2,-1,3,1},{-2,3,-1,-2},{3,-2,2,-1}};
MatrixForm[a]

a1={a[[1]],a[[1]]+a[[2]],3*a[[1]]-2*a[[3]]};
MatrixForm[a1]

a2={a1[[1]],a1[[2]],a1[[2]]-2*a1[[3]]};
MatrixForm[a2]

x3=11/8
x2=(-1-2*x3)/2
x1=(1+x2-3*x3)/2

Clear[x1,x2,x3];
aa={{2,-1,3},{-2,3,-1},{3,-2,2}};
x={x1,x2,x3};
b={1,-2,-1};
sys=Dot[aa,x]==b
Solve[sys,x]

(* ALTRO ESEMPIO *)

a={{1,-3,4,5},{2,3,4,-1},{5,-5,2,3},{-1,-2,7,6}};
MatrixForm[a]

a1={a[[1]],2a[[1]]-a[[2]],5*a[[1]]-a[[3]],a[[1]]+a[[4]]};
MatrixForm[a1]

a2={a1[[1]],a1[[2]],9*a1[[3]]-10*a1[[2]],9*a1[[4]]-5*a1[[2]]};
MatrixForm[a2]