Question

Please follow following scripts:

Matlab Exercises 1. Find the determinant (command: det(A)) and the condition number (command: cond(A)) of the Hilbert matrix H of order k (command: hilb(k)), for k = 1,2, ..., 10. Plot the determinant and the condition number as a function of k using a logarithmic scale for the vertical axis. Hint: The template to help you with this homework assignment is homework/hw15.m. 2. Determine if y is in the subspace of R4 spanned by the columns of A, where [ 3 -5 -9] 1 8 7 -6 1-5 -8 31 | 2 -2 -9 y = А Hint: The template to help you with this homework assignment is homework/hw25.m. Homework Problems

Script for part A:Script for Part B:

Answer 1

Part A

%% part A
clear, close all; clc;

n = 10;
id = zeros(n,1); % allocating vector for id
dA = zeros(n,1); % allocating vector for det A
cA = zeros(n,1); % allocating vector for cond A

% compute hilber matrix H and its determinant and
% store it in a vector to be able to plot it
for k = 1:n
A = hilb(k); % compute H of order k
  
% remember id(for plotting)
id(k) = k;
  
% store determinant(for plotting)
dA(k) = det(A);
  
% store condition number(for plotting)
cA(k) = cond(A);
  
% display the hilbert matrix
fprintf('hilbert matrix of order k=%i\n',k);
disp(A)
end
figure(1),plot(id,dA); % plot det
xlabel('id');
ylabel('det');
set(gca,'Yscale','log'); % make the vertical axis as log
figure(2),plot(id,cA); % plot det
xlabel('id');
ylabel('cond');
set(gca,'Yscale','log'); % make the vertical axis as log

84 part A clear, close all; clc; n = 10; id = zeros (n,1); A = zeros (n,1); CA = zeros(n,1); $ allocating vector for id $allocating vector for det A allocating vector for cond A * compute hilber matrix H and its determinant and store it in a vector to be able to plot it Çfor k = 1:n A = hilb(k); compute H of order k remember id(for plotting) id (k) = k; * store determinant (for plotting) JA (k) = det (A); store condition number (for plotting) CA (k) = cond(A); II III III III $display the hilbert matrix fprintf('hilbert matrix of order k=i\n', k); disp (A) end figure (1), plot(id, dA); $plot det xlabel('id'); ylabel('det'); set (gca, 'Yscale', 'log'); make the vertical axis as log figure (2), plot(id, CA); $plot det xlabel('id'); ylabel('cond'); set (gca, 'Yscale', 'log'); make the vertical axis as log

Output

100 10-10 10-20 10-30 10-404 10-50 10-60 1 2 3 4 5 6 7 8 9 10 id

1014 1012 1010 cond 100 1 2 3 4 5 6 7 8 9 10 id

Part - B

clear, close all;
y = [-4; -8; 6; -5]; % Enter the input
A = [ 3, -5, -9; ...
8, 7, -6; ...
-5, -8, 3; ...
2, -2, -9 ];
combinedMat= [y A]; % make a 4 x 4 matrix
if det(combinedMat) == 0 % if det is 0 then the column vectors are dependent
fprintf("y is in the subspace\n");
else
fprintf("y is not in the subspace\n");
end

** Part B clear, close all; y = (-4; -8; 6; -5]; $ Enter the input A = [ 3, -5, -9; ... 8, 7, -6; ... -5, -8, 3; ... 2, -2, -9]; combinedMat= (y A]; $make a 4 x 4 matrix if det (combinedMat) == 0 $ if det is o then the column vectors are dependent fprintf("y is in the subspace\n"); else fprintf("y is not in the subspace\n"); end Command Window y is not in the subspace