1. Verify the 3 digit floating point calculations for the 2 by 2 example with row interchange in the method section.
2. Use the Maple procedures Digits and cond to study the polynomial function approximation where f(1) = 1, f(1.1) = 2, f(1.11) = 3 and f(1.13) = 4 Use a third order polynomial, and vary the digits. Graph the polynomial whose coefficients are the accurate solution of the associated algebraic system.
3. Find the norm of x, norm of A and the cond(A) where
Use Maple to find the inverse of A and compare cond(A) with your hand calculated condition number of A with respect to the max norm.
4. Prove the first three basic properties of the max norm.