System of nonlinear equations! f(x) = (x_1)^5 + (x_2)^3 * (x_3)^4 + 1, (x_1)^2 * x_2

[bambus]

Hello guys. I need help for one math project.

Its about system of nonlinear equations. The system go like this:

. . . . .\(\displaystyle \large{f(x)\, =\, \begin{cases}{x_1}^5\, +\, {x_2}^3\, \cdot\, {x_3}^4\, +\, 1 \\ {x_1}^2\, \cdot\, x_2\, \cdot\, x_3 \\ {x_3}^4\, -\, 1 \end{cases}}\)

a) Calculate all the zero`s in the system (mannualy)
b) Find the Jacobioan matrix, J(x). (Notice that J(x) is singular for x(3) = 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 dont know if i am right...

Please help me. Thank you!

 

[stapel]

Hello guys. I need help for one math project.

Its about system of nonlinear equations. The system go like this:

. . . . .\(\displaystyle \large{f(x)\, =\, \begin{cases}{x_1}^5\, +\, {x_2}^3\, \cdot\, {x_3}^4\, +\, 1 \\ {x_1}^2\, \cdot\, x_2\, \cdot\, x_3 \\ {x_3}^4\, -\, 1 \end{cases}}\)

The above is one piecewise function, with no intervals defined for the pieces. This is not a "system of...equations".

Please reply with the full and exact text of the exercise.

a) Calculate all the zero`s in the system (mannualy)
b) Find the Jacobioan matrix, J(x). (Notice that J(x) is singular for x(3) = 0)

A "Jacobian" usually refers to something involving derivatives. However, you have posted this to an "Algebra" category. With what topic are you having difficulty?

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 dont know if i am right...

Unfortunately, it is not possible to check work that we cannot see. Please reply with a clear listing of all of your steps and results. Thank you!