(5 points) Consider the equations x+y+3x+u+v+4=0 xy-zu-v+3=0 around the point (x, y, z, u, v) =...

 

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(5 points) Consider the equations x+y+3x+u+v+4=0 xy-zu-v+3=0 around the point (x, y, z, u, v) = (1,0-1, -3, 1). Let F(x, y, z, u,v) = (x + y + 3 z+u+v+4, xy z +u-v+3)T. Use the implicit function theorem to show that there is a function g: U R where U is an open set containing (r, z,v) = (1, 1, 1), so that gi(x,z,v) = y, 92(x,z,v) = u and F(x, 91(x,z, v), z, 92(x, z, v), v) = (0, 0). Find Dg(1, -1, 1). (5 points) Consider the equations x+y+3x+u+v+4=0 xy-zu-v+3=0 around the point (x, y, z, u, v) = (1,0-1, -3, 1). Let F(x, y, z, u,v) = (x + y + 3 z+u+v+4, xy z +u-v+3)T. Use the implicit function theorem to show that there is a function g: U R where U is an open set containing (r, z,v) = (1, 1, 1), so that gi(x,z,v) = y, 92(x,z,v) = u and F(x, 91(x,z, v), z, 92(x, z, v), v) = (0, 0). Find Dg(1, -1, 1).