8. Let A be the 10 x n matrix formed by the first n columns of the 10 x 10 Hilbert matrix. Let c be the n-vector [1, ..., 1], and set b = Ac. Use the normal equations to solve the least squares problem Ax = b for solution x = c. How many correct decimal places can be computed? Use condition number to explain the results. (b) n = 8, and compare with the correct least squares

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8. Let A be the 10 x n matrix formed by the first n columns of the 10 x 10 Hilbert matrix.
Let c be the n-vector [1, ..., 1], and set b = Ac. Use the normal equations to solve the least
squares problem Ax = b for
solution x = c. How many correct decimal places can be computed? Use condition number to
(b) n = 8, and compare with the correct least squares
explain the results.
Transcribed Image Text:8. Let A be the 10 x n matrix formed by the first n columns of the 10 x 10 Hilbert matrix. Let c be the n-vector [1, ..., 1], and set b = Ac. Use the normal equations to solve the least squares problem Ax = b for solution x = c. How many correct decimal places can be computed? Use condition number to (b) n = 8, and compare with the correct least squares explain the results.
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