Let f : R → at (1, 2, 3)is given by the matrix R° be a C' function with f(x, y, z) = (u, v, w) and f(1, 2, 3) = (3, 4, 1). Suppose the Jacobian of f T1 3 2 [Jf(1, 2, 3)] 4 8 -1 9. 1 Since the determinant of Jf(1, 2, 3)] is which is non-zero, f has a C' inverse near (3, 4, 1). Compute the value of the following derivative:

Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 18CM
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Let f : R → R³ be a C' 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
[1
2
[Jf(1,2, 3)]
4
8
-1
%3D
4 9
1
Since the determinant of [Jf(1, 2, 3)] is
which is non-zero, f has a OC' inverse near (3, 4, 1). Compute the
value of the following derivative:
Transcribed Image Text:Let f : R → R³ be a C' 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 [1 2 [Jf(1,2, 3)] 4 8 -1 %3D 4 9 1 Since the determinant of [Jf(1, 2, 3)] is which is non-zero, f has a OC' inverse near (3, 4, 1). Compute the value of the following derivative:
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