Prove a partial converse to Theorem 5 1 If MCRn is a k dimensional manifold and x 1028 M, then there is an open set A C Rn containing and a differentiable function g A Rn k such that AM g 1 (0) and g1 (y) has rank n k when g(y) 0

Question: Prove a partial converse to Theorem 5-1: If MCRn is a k-dimensional manifold and xЄM, then there is an open set A C Rn containing

Prove a partial converse to Theorem 5-1: If MCRn is a k-dimensional manifold and xЄM, then there is an open set A C Rn containing and a differentiable function g: A →Rn-k such that A∩M = g-1 (0) and g1 (y) has rank n – k when g(y) = 0.

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