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1. Determinant
2. Singularity
3. Orthogonality
4. Inverse
5. Transpose
6. Square of matrix
4. Eigne values and eigen vectors
6. Rank of a matrix

Code:

clc

close all

clear all

% A = [1 -2i; 1i -2]; % Given matrix

A = [1 2 3; 0 1 5; 5 6 0]

detA = det(A); % Determinant

fprintf('The determinant is:\n');

disp(detA);

%% Check for singularity with conditional statement

if detA == 0

fprintf('The given matrix is singular\n');

else

fprintf('The given matrix is non singular\n');

end

%% Check for orthogonality with conditional statement

if detA == 1 || detA == -1

fprintf('The given matrix is orthogonal\n');

else

fprintf('The given matrix is non orthogonal\n');

end

invA = inv(A); % Inverse

fprintf('The inverse is:\n');

disp(invA);

transA = transpose(A); % Transpose

fprintf('The transpose is:\n');

disp(transA);

squareA = A*A; % Square value of matrix

fprintf('The square of given matrix is:\n');

disp(squareA);

%% Eigne values and Eigne vectors

eigVal = eig(A); % Eigen values

fprintf('The eigen values are:\n');

disp(eigVal);

% or

[V D] = eig(A); % Eigen vectors and eigen velues

fprintf('The eigen vector and eigen values are:\n');

disp(V);

disp(D);

%% Rank

rankA = rank(A);

fprintf('The rank is:\n');

disp(rankA);

A =

1     2     3

0     1     5

5     6     0

The determinant is:

5.0000

The given matrix is non singular

The given matrix is non orthogonal

The inverse is:

-6.0000    3.6000    1.4000

5.0000   -3.0000   -1.0000

-1.0000    0.8000    0.2000

The transpose is:

1     0     5

2     1     6

3     5     0

The square of given matrix is:

16    22    13

25    31     5

5    16    45

The eigen values are:

-5.6418

-0.1143

7.7561

The eigen vector and eigen values are:

0.1769   -0.7592   -0.4704

0.5919    0.6353   -0.5250

-0.7863   -0.1416   -0.7093

-5.6418         0         0

0   -0.1143         0

0         0    7.7561

The rank is:

3

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