Let f : R³ → R³ be a C¹ function with f(x, y, z) = (u, v, w) and f(1, 2,3) = (3,4, 1). Suppose the Jacobian of f at (1, 2, 3) is given by the matrix
| 3 -7 8 |
[Jf(1, 2,3)] = |-2 4 -3 |
|-4 5 5 |
Since the determinant of [Jf(1, 2, 3)] is ____ which is non-zero, f has a C¹ inverse near (3, 4, 1). Compute the value of the following derivative: dz/dv