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 10^k (with k a positive integer), then the computed solution of Ax = b should usually be accurate to at least r - k significant digits.

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.

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A 1 1/2 1/2 1/3 1/3 1/4 1/4 1/5 1/5 1/6 1/3 1/4 1/4 1/5 1/6 1/7 1/7 1/5 1/5 1/6 1/6 1/7 1/7 1/8 1/8 1/9