Let n >= 3 be an integer. Let Vn(x) = {[x 1 1 1 ... 1 1]T,[1 x 1 1 ... 1 1]T, [1 1 x 1 ... 1 1]T, ... , [1 1 1 x ... 1 1]T, [1 1 1 1 ... x 1]T, [1 1  1 1 ... 1 x]T} be contained in Rn. (a) For what values of x does Vn(x) fail to be a basis for Rn? (b) For each such value of x found in (a), what is the dimension of span(Vn(x))?

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