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Unformatted text preview: Q R, where R = p R 11 R 12 P , and R 11 is an invertible r r upper-triangular matrix. Also show that the Frst r columns of Q form a basis for the column-space of A . In what fundamental sub-space of A do the last m r columns of Q lie? Do they form a basis for that space? 6. Assuming A has full column-rank, show how to use the Q R factorization of A from problem 5 to compute the least-squares solution min x b A x b b 2 . 7. Assuming A has full row-rank, show how to use the Q R factorization of A T from problem 5 to Fnd the minimum-norm solution min Ax = b b x b 2 . 1...
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- Fall '08