Given the system of equations below, complete parts a, b, c, and d.F(x,y,z,u,v,w) = 11x – 3y – 6z2 – 3u + 6v2 – 477 = 0G(x,y,z,u,v,w) = 22x - 6y + 5z + 5u? - 3v + 20w - 328 = 0H(x,y,z,u,v,w) = 4x + 4z + 4u? + 16w - 344 = 0a(F,G,H)a(F,G,H)anddu,v,w)(a) Calculate the Jacobiansd(x,y,z)a(F,G,H)d(x.y,z)d(F,G,H)(Simplify your answer.)d(u,v,w)(b) Is the system of equations solvable for u, v, w as functions of x, y, z near the point P, where (x,y,z) = (-6, - 5, - 4) and (u,v,w) = (- 8,10,8)? Explain.a(F,G,H)Ə(F,G,H)O A. Yes, becauseis not zero.O B. No, becauseis zero.d(x,y,z)d(u,v,w)a(F,G,H)Ə(F,G,H)O C. No, becauseis not zero.O D. Yes, becauseis zero.a(u,v,w)d(x,y,z)d(F,G,H)a(F,G,H)O E. Yes, becauseis not zero.O F. No, becauseis zero.a(u,v,w)d(x,y,z)(c) Calculatedzx,yat (x,y,z) = (- 6, - 5, – 4).(Simplify your answer.)(d) What is the condition that will guarantee the system of equations is solvable for x, y, z as functions of u, v, w?The condition that will guarantee the system of equations is solvable for x, y, z as functions of u, v, w is1. (Simplify your answer.)

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Given the system of equations below, complete parts a, b, c, and d. F(x,y,z,u,v,w) = 11x- 3y – 6z² – 3u + 6v² – 477 = 0 G(x,y,z,u,v,w) = 22x – 6y + 5z + 5u - 3v + 20w – 328 = 0 H(x,y,z,u,v,w) = 4x+ 4z + 4u? + 16w - 344 = 0 a(F,G,H) Ə(F,G,H) and d(u,v,w) (a) Calculate the Jacobians a(x,y,z) d(F,G,H) d(x,y,z) d(F,G,H) (Simplify your answer.) d(u,v,w) (b) Is the system of equations solvable for u, v, w as functions of x, y, z near the point P, where (x,y,z) = (– 6, - 5, – 4) and (u,v,w) = (- 8,10,8)? Explain. d(F,G,H) d(x,y,z) Ə(F,G,H) a(u,v,w) O A. Yes, because is not zero. O B. No, because is zero. Ə(F,G,H) d(F,G,H) OC. No, because -is not zero. O D. Yes, because is zero. d(u,v,w) d(x,y,z) Ə(F,G,H) (F,G,H) O E. Yes, because is not zero. OF No, because is zero. d(u,v,w) d(x,y,z) du (c) Calculate at (x,y,z) = (- 6, – 5, – 4). dz )x.y (Simplify your answer.) (d) What is the condition that will guarantee the system of equations is solvable for x, y, z as functions of u, v, w? The condition that will guarantee the system of equations is solvable for x, y z functions of u, v, w is 1. (Simplify your answer.)