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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!

Bambus
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  • So it seems you have completed (a). For (b), do you know what a Jacobian matrix is? – Matthew Leingang Apr 03 '17 at 17:08
  • @MatthewLeingang Well i agree with Moo answer. I know how is going now. But what to do for C) ? (Is allowed to use newton method). – Bambus Apr 03 '17 at 17:42
  • @Moo Can you explain me in some steps how its going for this example? Because i havent worked with this... – Bambus Apr 03 '17 at 17:43

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