Q1 Hadamard's inequality (i) Let A = (a lan) E Rnxn. Let A = QR = Q(r|rn) be a QR factorization of A. - First, show that det(A)| II ri||2. Then, using the previous part, show that det(A)| II1 |ai||2. This inequality is known as "Hadamard's inequality". - (ii) Let A = (a,j) Rnxn with aj {-1, 1} Vi, je {1,...,n}. Using (i), show that det(A)| n. (iii) Show that if A Rx" is a Hadamard matrix, then [det(A) = n*.