Solve question 10.18 using MATLAB code. How many digits k meat a). but scale the

Question

Solve question 10.18 using MATLAB code. How many digits k meat a). but scale the matrix by making of pre the od hematrix by makingthe the maximum ele nt in each row equal to one. 10.16 Determine the condition number based o for the normalized 4 x 4 Hilbert matrix. Hou digits of precision will be lost due to ill-condion /decomposition: / decomposition(b) Repeat (a), but scale the matrix by ma on the row-sum ow to ill-conditioni out pivoting by 10.17 Besides the Hilbert matrix, there are othig lts by validating inherently ill-conditioned. One such case ng? gnif matrix, which has the following form .r x X2 2 x3 n the row-sum nom nant.(c) Repeat (a) Determine the condition number based on the row for the case where X1 = 4, x2 = 2, and n = 7 software to compute the spectral ompute the de (b) Use MATLAB or Mathcad software to co /and Frobenius condition numbers 10.18/ Develop a user-friendly program for LU decomposition 10 44-26]. 1044-26), bised on the pseudocode from Fig. 10.2. 33-4.6667 9/Develop a user-friendly program for L// decomposition, in- 0.1 ng the capability to evaluate the matrix inverse. Base the pro- gram on Figs. 10.2 and 10.5. 10.20 Use iterative refinement techniques to improve x2 36364 -3, and x-8, which are approximate solutions of 2x1 + 5x2+X3 =-5 5 x2 = +2x2 + x3 = 12 x1 +2x2 + x3 = 3 t in each row orms for the ymaking the ymakingthe B=A+j-4k 10.21 Consider vectors: Ai-3j+ak Asa-Ij+ak Vector A is perpendicular to B as well as to C. It is also B-C=2, three unknowns, a, b, and c. 10.22 Consider the follou o known that Chapter to solve for the Use any method studied in this chapter to nsides a ethod tiuas well ned in is to ltis number and

Explanation / Answer

function [L,U,P]=LU_pivot(A)
% LU factorization with partial (row) pivoting
% K. Ming Leung, 02/05/03

[n,n]=size(A);
L=eye(n); P=L; U=A;
for k=1:n
    [pivot m]=max(abs(U(k:n,k)));
    m=m+k-1;
    if m~=k
        % interchange rows m and k in U
        temp=U(k,:);
        U(k,:)=U(m,:);
        U(m,:)=temp;
        % interchange rows m and k in P
        temp=P(k,:);
        P(k,:)=P(m,:);
        P(m,:)=temp;
        if k >= 2
            temp=L(k,1:k-1);
            L(k,1:k-1)=L(m,1:k-1);
            L(m,1:k-1)=temp;
        end
    end
    for j=k+1:n
        L(j,k)=U(j,k)/U(k,k);
        U(j,:)=U(j,:)-L(j,k)*U(k,:);
    end
end

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