We have a subset X, which is contained in R^4 (i.e., it is contained in the reals in 4 dimensions).(adsbygoogle = window.adsbygoogle || []).push({});

(a) We must prove that the following two equations represent a manifold in the neighborhood of the point a = (1,0,1,0):

(x_1)^2+(x_2)^2-(x_3)^2-(x_4)^2=0 and x_1+2x_2+3x_3+4x_4=4.

(b) Also we must find a tangent space to X at a.

(c) We must find a pair of variables that the equations above do not express as functions of the other two.

(d) We must determine whether the enter set X is a manifold and prove the conclusion.

How do you do this problem?

Thanks.

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# Manifold Problems

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