Suppose you are given an n n symmetric matrix of positive numbers, D with 0's along the diagonal. Is it always possible to find a collection of n points (xi, yi), i = 1, . . . , n so that the Euclidean distance between (xi, yi) and (xj , yj ) is Dij ? Either argue that this is possible or give an example that shows it is not.

Suppose you are given an n X n symmetric matrix of positive numbers, D with 0's along the diagonal. Is it always possible to nd a collection of n points (magi), i = 1,. . . ,n so that the Euclidean distance between ($1335) and (5173-, yj) is D35? Either argue that this is possible or give an example that shows it is not