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...Problem set matrix calculus m phil premath september matrices are typically used to represent big systems of linear equations course one can use in such let f x be a scalar function the n then is an whose i j th element xij exercise denote two vectors ax show that if denotes and vector verify take xax where compute xx symmetric b using formula from excercise suppose for given y k full column rank we want nd coecients combination e xb isclosesttovectory minimise ky xbk hy xbi wecanproceed ways which this derivation zero so called orthogonal projection theorem says argminky isorthogonal any r have whichsatises following orthogonality conditions d...