Exercises 42–44 show how to use the condition number of a matrix A to estimate the accuracy of a computed solution of Ax = b. If the entries of A and b are accurate to about r significant digits and if the condition number of A is approximately 10k (with k a positive integer), then the computed solution of Ax = b should usually be accurate to at least r – k significant digits.
[M] Solve an equation Ax = b for a suitable b to find the last column of the inverse of the fifth-order Hilbert matrix
How many digits in each entry of x do you expect to be correct? Explain. [Note: The exact solution is (630, ––12600, 56700, –88200, 44100).]
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