Question

1. An n x n matrix is said to be diagonally dominant if , lail for i = 1,...,n ji Basically, if for every row, the absolute value of the entry along the main diagonal is larger than the sum of the absolute values of all other entries on that row. Write a function whose input is a matrix and will determine (true/false) if a matrix is diagonally dominant. Show that your function works as expected.

Please answer through MATLAB and show WHOLE script.

Answer 1

MATLAB code:

%----------------------

function result = dominant(A)
% matrix dimensions
d = size(A);
% for loop over rows
for i = 1:d
% sum of row elements except diagonal element
sum_row =0;
% for loop over columns
for j = 1:d
% adding each elements to sum variable
sum_row = sum_row+ abs(A(i,j));
end
%subratcting diagonal element
sum_row = sum_row-abs(A(i,i));
%checking dominant condition
% failed once means matrix is not diagonal dominant
if abs(A(i,i))< sum_row
result = 'false';
return;
end
end

% dominant condition not failed
result = 'true';
end

% matrix A
A = [ 3 -2 1; 1 -3 2; 1 2 6]

% result
result = dominant(A)

% matrix A
A = [ -2 1 2; 1 3 2; 1 -2 0]

% result
result = dominant(A)

%----------------------

Output:

A = 3 1 1 -2 -3 2 Nm 1 2 6 result = true A = -2 - 1 3 1 -2 1 2 2 o result = false

Code snippet:

function result = dominant(A) % matrix dimensions d = size(A); % for loop over rows for i = 1:0 % sum of row elements except diagonal element sum_row =0; % for loop over columns for j = 1:0 % adding each elements to sum variable sum_row = sum_row+ abs(A(ij)); end %subratcting diagonal element sum_row = sum_row-abs(A(1,1)); %checking dominant condition % failed once means matrix is not diagonal dominant if abs(A(i,i))< sum_row result = 'false'; %return; end end result = 'true'; end % matrix A A = (3-21; 1-3 2; 1 2 6) % result result = dominant(A) % matrix A A = (-21 2; 1 3 2; 1-20) % result result = dominant(A)