I need help for one math project.
It's about a system of non-inear equations. The system go like this:
$$ f(x)=\left\{ \begin{array}{ll} x^5+y^3*z^4+1 \\ x^2*y*z \\ z^4-1 \end{array} \right. $$
The right side of the equation is 0.
a) Calculate all the zeros in the system (manually)
b) Find the Jacobian matrix, J(x). (Notice that J(x) is singular for z = 0)
c) Consider independent two starting solutions:
1) x(0) = {-0.01, -0.01, -0.01}T
2) x(0) = {-0.1, -0.1, -0.1}T
I have tried something but I don't know whether I am right...
$$ f(x)=\left\{ \begin{array}{ll} x^5+y^3*\pm1=-1 \\ x^2*y*\pm1=0 \\ z=\pm1 \end{array} \right. $$
So because in the middle line there is 0 in the right side some of X and Y must be 0. When i get for Y=0 the result is this: $$x= -1 , y= 0, z= \pm1$$
And for X=0 the result is this: $$x= 0 , y= -1, z= \pm1$$
I dont know where to go after this...
Please help me. Thank you!