Consider the ill-conditioned system:
.835x + .667y = .168,
.333x + .266y = .067.
(a) Describe the outcome when you attempt to solve the system using 5-digit arithmetic with no scaling.
(b) Again using 5-digit arithmetic, first row scale the system before attempting to solve it. Describe to what extent this helps.
(c) Now use 6-digit arithmetic with no scaling. Compare the results with the exact solution.
(d) Using 6-digit arithmetic, compute the residuals for your solution of part (c), and interpret the results.
(e) For the same solution obtained in part (c), again compute the residuals, but use 7-digit arithmetic this time, and interpret the results.
(f) Formulate a concluding statement that summarizes the points made in parts (a)-(e).