We have a subset X, which is contained in R^4 (i.e., it is contained in the reals in 4 dimensions). (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.