Consider the function F: R5 → R² given by F(x, y, z, u, v) = ( 3 (№ry ³). xy + xuv + uv². u²v + xuv 2 v(x, y, z) o (1, 1, 1, 1, 1). Clearly state which result(s) you Prove that u and v can be expressed as functions u = u(x, y, z) and v= x, y, z near the point (x, y, z, u, v) are using. =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Consider the function F : R5 → R² given by
F(x, y, z, u, v)
=
xy + xuv + uv² – 3`
u²v + xuv - 2
Prove that u and u can be expressed as functions u = u(x, y, z) and v = v(x, y, z) of
x, y, z near the point (x, y, z, u, v) = (1, 1, 1, 1, 1). Clearly state which result(s) you
are using.
Transcribed Image Text:Consider the function F : R5 → R² given by F(x, y, z, u, v) = xy + xuv + uv² – 3` u²v + xuv - 2 Prove that u and u can be expressed as functions u = u(x, y, z) and v = v(x, y, z) of x, y, z near the point (x, y, z, u, v) = (1, 1, 1, 1, 1). Clearly state which result(s) you are using.
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