I am having some issue with a Linearly separation problem that has been going around on my head. I am pretty positive it's true, but not sure how to prove it.

Given k points in a n-dimension linearly separable by a hyperplane H:

$w1*x1 + w2*x2 + ... + wn*xn + B = 0 $

Show that when projecting the k points onto 2D planes, then there must exist at least 1 plane P in which the projection of those points are linearly separable.

Also, a bit extra but, in that plan whose projection is separable, can the line which separate the points have any correlation with the hyperplane H. Like many lines can separate the points, but there exist a line that is parallel to the intersection line of hyperplane H and plane P.

Thanks in advance.



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