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3. Consider the simultaneous equations fi(z, y. 2) = (ry- - 1) = 0, f2(x, y, 2) = (xy² +z2-15y) = 0, f3(x, y, =) = (2y² +? – 6) = 0. %3D (a). Obtain the Jacobian matrix for the system of equations.

3. Consider the simultaneous equations fi(z, y. 2) = (ry- - 1) = 0, f2(x, y, 2) = (xy² +z2-15y) = 0, f3(x, y, =) = (2y² +? – 6) = 0. %3D (a). Obtain the Jacobian matrix for the system of equations.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section9.7: The Inverse Of A Matrix
Problem 32E
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3. Consider the simultaneous equations fi(z, y, 2) = (ry-- 1) = 0, f2(r, y, :) = (ry² +xz? – 15y) = 0, fa(x, y, =) = (2y² + :² - 6) = 0. %3D %3D %3D %3D (a). Obtain the Jacobian matrix for the system of equations. (b). For initial guesses r = 2, y = 2, and z = 2, obtain one solution, a set of r, y, and 2, using Matlab function fsolve. (c). Obtain a master equation in y by expressing 2² in terms of y, r in terms of y, and finally two relations for z in terms of y. Identify all roots of the master equation using the Matlab function roots(coeff). Obtain the corresponding z and z. (d). Try to obtain all real roots of the system of equations using Matlab function fsolve.
Transcribed Image Text:3. Consider the simultaneous equations fi(z, y, 2) = (ry-- 1) = 0, f2(r, y, :) = (ry² +xz? – 15y) = 0, fa(x, y, =) = (2y² + :² - 6) = 0. %3D %3D %3D %3D (a). Obtain the Jacobian matrix for the system of equations. (b). For initial guesses r = 2, y = 2, and z = 2, obtain one solution, a set of r, y, and 2, using Matlab function fsolve. (c). Obtain a master equation in y by expressing 2² in terms of y, r in terms of y, and finally two relations for z in terms of y. Identify all roots of the master equation using the Matlab function roots(coeff). Obtain the corresponding z and z. (d). Try to obtain all real roots of the system of equations using Matlab function fsolve.
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