Returning to a general matrix X, show that if the label vector y is a linear combination of the {ui}ri=1 then there exists a w for which the empirical risk is zero (meaning Xw = y). Hint: Either consider the range of X and use the SVD, or compute the empirical risk explicitly with y = Pri=1 aiui for some constants ai and w ols = X+y. Remark: It's also not hard to show that if y is not a linear combination of the {ui}ri=1, then the empirical risk must be nonzero