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April 2nd, 2017, 01:20 PM  #1 
Newbie Joined: Apr 2017 From: Macedonia Posts: 3 Thanks: 0  System of nonlinear equations!
Hello guys. I need help for one math project. It's about a system of noninear equations. The system go like this: a) Calculate all the zeros in the system (manually) b) Find the Jacobian 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 don't know whether I am right... Please help me. Thank you! Last edited by skipjack; April 3rd, 2017 at 06:17 AM. 
April 2nd, 2017, 02:49 PM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,354 Thanks: 591 
Well, what did you try? A couple of obvious points from $\displaystyle x_3^4 1= 0$ we have $\displaystyle x_3^4= 1$ and so $\displaystyle x_3= 1$, $\displaystyle x_3= 1$, $\displaystyle x_3= i$, or $\displaystyle x_3= i$ (the last two if you are looking for solutions in the complex numbers). And, of course, since $\displaystyle x_1x_2x_3= 0$ must have $\displaystyle x_1= 0$ or $\displaystyle x_2= 0$ (since we have already determined that $\displaystyle x_3$ cannot be 0). Last edited by skipjack; April 3rd, 2017 at 06:21 AM. 
April 2nd, 2017, 03:56 PM  #3 
Senior Member Joined: Oct 2013 From: New York, USA Posts: 502 Thanks: 74 
Rather than use subscripts, I'm going to use x for x1, y for x2, and z for x3. If somebody would like to redo my post using subscripts, that's fine with me. Assuming we're only working with real numbers, substituting Country Boy's value of z in the first equation makes it an equation with an x term, a y term (with a coefficient of 1 that drops out), and a constant. Make the right side have the constant. As Country Boy said, x or y must be 0, and you can substitute in 0 for x and solve for y and sub in 0 for y and solve for x.

April 3rd, 2017, 06:04 AM  #4  
Newbie Joined: Apr 2017 From: Macedonia Posts: 3 Thanks: 0  Quote:
I tried to make it like you said, and for y=0 in the end i am getting x=1, y=0 and z= +1, and when i put x=0 i am getting y=+1, x=0, z=+1  
April 3rd, 2017, 06:06 AM  #5  
Newbie Joined: Apr 2017 From: Macedonia Posts: 3 Thanks: 0  Quote:
I tried to make it like you said, and for x2 = 0 in the end I am getting x1 = 1, x2 = 0 and x3 = ±1, and when I put x1 = 0 I am getting x2 = ±1, x1 = 0, x3 = ±1 Last edited by skipjack; April 3rd, 2017 at 06:23 AM.  

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