The Hilbert matrix is a classic example of a badly conditioned matrix: Small changes in their coefficients cause large changes in the solution of the disturbed system. Calculate the exact solution of AX = B (Leaving all numbers as fractions and use exact arithmetic) where 1 A = B = 6

The Hilbert matrix is a classic example of a badly conditioned matrix: Small changes in their coefficients cause large changes in the solution of the disturbed system. Calculate the exact solution of AX = B (Leaving all numbers as fractions and use exact arithmetic) where 1 A = B = 6

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

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The Hilbert matrix is a classic example of a badly conditioned matrix: Small changes in their
coefficients cause large changes in the solution of the disturbed system.
Calculate the exact solution of AX = B (Leaving all numbers as fractions
and use exact arithmetic) where
1
A
В
Now solve the system AX = B using arithmetic rounding to four decimal places.

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