Consider the System

f1(x1,x2,x3)=3x1-cos(x2x3)-1.2=0
f2(x1,x2,x3)=x1^2-81(x2+0.1)^2+sinx3+1.06=0
f3(x1,x2,x3)=e^-x1x2+20x3+ (10-3)/3=0

(1) find y^(k-1) and solve the linear system J(x^(k-1))y^(k-1)=-F(x^(k-1))
When J(x)= 3 x3sinx2x3 x2sinx2x3
2x -162(x2+0.1) cosx3
-x2e^-x1x2 -x1e^-x1x2 20

Newton Method and Jacobian using mathematica