I have the following question from multivariable analysis, please if able explain in steps, thank you in advance: Let Id be the identity map in R" and let f : R → R be the functionf(x) = ||||2. Prove that the function G := fId: R → R" is a differentiable bijection that satisfies:• DG(0) = 0,• DG(p) has non-zero determinant for all other p.. The inverse of G is not differentiable at 0.

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Let Id be the identity map in R" and let f : R → R be the function f(x) = ||||². Prove that the function G := fId : R" → R" is a differentiable bijection that satisfies: • DG(0) = 0, • DG(p) has non-zero determinant for all other p. The inverse of G is not differentiable at 0.

Let Id be the identity map in R" and let f : R → R be the function f(x) = ||||². Prove that the function G := fId : R" → R" is a differentiable bijection that satisfies: • DG(0) = 0, • DG(p) has non-zero determinant for all other p. The inverse of G is not differentiable at 0.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.4: Spanning Sets And Linear Independence

Problem 76E: Let f1(x)=3x and f2(x)=|x|. Graph both functions on the interval 2x2. Show that these functions are...

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I have the following question from multivariable analysis, please if able explain in steps, thank you in advance:

Let Id be the identity map in R" and let f : R → R be the function
f(x) = ||||2. Prove that the function G := fId: R → R" is a differentiable bijection that satisfies:
• DG(0) = 0,
• DG(p) has non-zero determinant for all other p.
. The inverse of G is not differentiable at 0.

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