The second page is a continuation of the first page. The third page is the Theorem to which the problem refers. Thank you.

Exercise 2.4.4 If the matrix is large, we prefer to estimate the condition number instea trying to compute it exactly. Using MATLAB, solve a system Ax-b, where A iS large discrete Laplacian operator: m- 50; % Make m larger or smaller, as needed. A delsq(numgrid ('N',m)) n = size (A,1) b = ones (n,1); % 'all ones', right-hand side. ca -condest (A) Compute the norm of the residual, and use condes t and Theorem 2.4.1 to estimate t Since condest estimates the 1-condition number k1 (A), use 1-norms in our estimate. Theorem 2.4.1 Let Abe nonsingular, let b0, andlet x be an approximation to the solution of Ax = b. (In other words, let x be any vector whatsoever.) Let-b-Ai. Then lla