Question

Develop a function qr solve that solves an n × n system using the MATLAB reduced QR decomposition, if the matrix is singular, the QR decomposition will complete with no error. Make the return values [x, resid], where resid is the residual Ax -bll2. A large residual will indicate that the matrix is singular or ill-conditioned. Apply the function to solve each system -713 L 21 3-481 「11 1 3 59 0 I1.1 2 -22 35 378 100 3」 L2 r-

Develop a function QR deceomposition using MATLAB and solve this system

Answer 1

Solution:-

I have written the required code below:-

A = [1 -1 0; 2 4 5; -7 1 3];

B = [1 -1 8]';

% Solving required matrices

[x1, resi1] = qr_decomp(A, B);

C = [21 3 -4 8; 1 3 59 0; 1 2 -22 35; 3 78 100 3];

D = [1 -1 1 2]';

[x2, resi2] = qr_decomp(C, D);

% Printing results

x1

resi1

x2

resi2

% Function to calculate QR decomposition and residual

function [X, resi] = qr_decomp(A, B)

[Q, R] = qr(A);

X = inv(R)*(Q')*B;

resi = (A*X - B).^2;

end

1 A-[1-1 0; 2 4 5; -7 1 3]; % solving required matrices 4[x1, resi1]-qr_decomp (A, B); 1.00 5 6 C-[21 3 -4 8; 1 3 59 0; 1 2 -22 35; 3 78 100 3]; 7 D [1 -1 1 2]'; 8 [x2, resi2]-qr_decomp (C, D); x1-3x1 -0.7500 9 1.7500 1.500e % Printing results 10 12 resil resi1 3x1 10-28x 13 x2 0.0493 resi2 14 0.1425 0.0710 15 x2 4x1 0.0321 0.0496 % Function to calculate QR decomposition and residual 16 0.8200 0.0122 function [X, resi] - qr_decomp (A, B) 17 resi24x1 o, R]r(A); 18 29 19 0.0197 resi - (A*X - B).*2; end 20 0.2416 0.0049 8.3155

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