Question: 22.4. (a) Suppose PA = LU (LU factorization with partial pivoting) and A = QR (QR factorization). Describe a relationship between the last row of

22.4. (a) Suppose PA = LU (LU factorization with partial pivoting) and A = QR (QR factorization). Describe a relationship between the last row of L1 and the last column of Q. (b) Show that if A is random in the sense of having independent, normally distributed entries, then its column spaces are randomly oriented, so that in particular, the last column of Q is a random unit vector. (c) Combine the results of (a) and (b) to make a statement about the nal rev.r of L"1 in Gaussian elimination applied to a random matrix A

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