Answered: Let W(s,t)=F(u(s,t),v(s,t)) where…

Intermediate Algebra

19th Edition

ISBN:9780998625720

Author:Lynn Marecek

Publisher:Lynn Marecek

Chapter4: Systems Of Linear Equations

Section4.6: Solve Systems Of Equations Using Determinants

Problem 279E: Explain the steps for solving a system of equations using Cramer’s rule.

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Let W(s,t)=F(u(s,t),v(s,t)) where

u(1,0) = -8, u_s(1,0) = 7, u_t(1,0) = -9
v(1,0) = -5, v_s(1,0) = -7, v_t(1,0) = 2
F_u(-8, -5) = 9, F_v(-8, -5) = 6

W_s(1,0)=? W_t(1,0)=?

Expert Solution

Step 1

Partially differentiate w with respect to s and t by chain rule of differentiation, we have

$\frac{\partial w (s, t)}{\partial s} = \frac{\partial F (u (s, t), v (s, t))}{\partial u} \frac{\partial u (s, t)}{\partial s} + \frac{\partial F (u (s, t), v (s, t))}{\partial v} \frac{\partial v (s, t)}{\partial s} a n d, \frac{\partial w (s, t)}{\partial t} = \frac{\partial F (u (s, t), v (s, t))}{\partial u} \frac{\partial u (s, t)}{\partial t} + \frac{\partial F (u (s, t), v (s, t))}{\partial v} \frac{\partial v (s, t)}{\partial t}$

so, we have

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Let W(s,t)=F(u(s,t),v(s,t)) where u(1,0) = -8, us(1,0) = 7, ut(1,0) = -9 v(1,0) = -5, vs(1,0) = -7, vt(1,0) = 2 Fu(-8, -5) = 9, Fv(-8, -5) = 6 Ws(1,0)=? Wt(1,0)=?