(f1, f2, f3,respectively): You are given the following systems of equations -xz- x3+4=0 2y5y-6=0 -2-2-3=0 (a)...

 

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(f1, f2, f3,respectively): You are given the following systems of equations -xz- x3+4=0 2y5y-6=0 -2-2-3=0 (a) Find the Jacobian, F, of this system. Let x = (!). fi Recall that: Fij = Jx j (b) Plug the values = y = 2; z = 1 into the Jacobian and use Gauss Elimination to compute the matrix inverse, F. How can the inverse Jacobian be used to solve the system of equations? (c) Express the system of equations in the form Ax = Ar taking the inverse Jacobian F-1 as your A matrix. Use the power method to estimate the largest eigenvalue. Start with the vector 1 y 2 and carry out three iterations of the power method. Calculate the percent relative error between iterations 1 & 2 and 2 & 3. If you did not calculate the inverse Jacobian, take 2.33 -1.75 0.13 A= -4.67 2.33 -1.75 0.13 -4.67 2.33 (f1, f2, f3,respectively): You are given the following systems of equations -xz- x3+4=0 2y5y-6=0 -2-2-3=0 (a) Find the Jacobian, F, of this system. Let x = (!). fi Recall that: Fij = Jx j (b) Plug the values = y = 2; z = 1 into the Jacobian and use Gauss Elimination to compute the matrix inverse, F. How can the inverse Jacobian be used to solve the system of equations? (c) Express the system of equations in the form Ax = Ar taking the inverse Jacobian F-1 as your A matrix. Use the power method to estimate the largest eigenvalue. Start with the vector 1 y 2 and carry out three iterations of the power method. Calculate the percent relative error between iterations 1 & 2 and 2 & 3. If you did not calculate the inverse Jacobian, take 2.33 -1.75 0.13 A= -4.67 2.33 -1.75 0.13 -4.67 2.33