Consider the matrix C = I„ — -J n , where I„ € M.n

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n is the identity matrix and Jn G Rn , n is a matrix consisting of 1. This matrix is called a centering matrix, since x TC = {xi — x}, where x = [χχ,χ^, · ■ ■, xn] is a vector of observations. Prove this fact. Also prove that J > i - xf = x TCx t = l