Create the following functions in MATLAB: function D=inverses(A) which takes as

Question

Create the following functions in MATLAB: function D=inverses(A) which takes as an input annex matrix A. First, the function has to determine whether A is invertible (you may want to use the function rank to do that). If A is not invertible, the function has to return an empty matrix d=[]; and terminates with a message "Matrix A is not invertible". If A is invertible, then the function reduces the matrix [A eye(n)] into the reduced echelon form and returns the matrix D that is the inverse of the matrix A. You can use a MATLAB built-in function rref for this part. **Type the functions inverses in your diary file. **Run the function D=inverses(A) on the given choices of the matrices A in (a)-(d). A = [4 -6 7 -1 0 1 -5 2 -7 11 10 3 -7 9 19 -1] A = [1 -3 2 -4 3 9 -6 12 2 -1 4 2 -4 5 -3 7], A = magic (5) **Run a built-in MATLAB function inv on the matrices A for parts (c) and (d). % Write a comment in you diary file why the result obtained by using inv function is inaccurate for the matrix in part (d).

Explanation / Answer

The MATLAB function for the finding inverse is given below:

%%function definition starts here:

%% Inverse finding

function D=inverses(A)

detA=det(A);

if detA==0

disp(' A is not Invertible');

D=[];

else

n=size(A);

B=[A eye(n)];

D_A=rref(B);

D=D_A(:,n+1:2*n);

end

%% function definition ends here

%% MATLAB code to run function

clc;

close all;

clear all;

%%

disp('Solution for a');

A=[4 0 -7 -7

-6 1 11 9

7 -5 10 19

-1 2 3 -1];

disp('Using inverses function');

inv_A=inverses(A);

disp(inv_A);

disp('Using MATLAB function inv()');

inv_matlab=inv(A);

disp(inv_matlab);

%% Solution for b

disp('Solution for b');

A=[1 -3 2 -4

-3 9 -1 5

2 -6 4 -3

-4 12 2 7];

disp('Using inverses function');

inv_A=inverses(A);

disp(inv_A);

disp('Using MATLAB function inv()');

inv_matlab=inv(A);

disp(inv_matlab);

%% Solution for c

disp('Solution for c');

A=magic(5);

disp('Using inverses function')

inv_A=inverses(A);

disp(inv_A);

disp('Using MATLAB function inv()');

inv_matlab=inv(A);

disp(inv_matlab);

%% Solution for d

disp('Solution for d');

A=magic(4);

disp('Using inverses function')

inv_A=inverses(A);

disp(inv_A);

disp('Using MATLAB function inv()')

inv_matlab=inv(A);

disp(inv_matlab);

disp(' The inv function fails if determinant of matrix is close to zero. Matrix is close to singular or badly scaled. Results may be inaccurate')

OUTPUT:

Solution for a

Using inverses function

-19 -14 0 7

-549 -401 -2 196

267 195 1 -95

-278 -203 -1 99

Using MATLAB function inv()

-19.0000 -14.0000 -0.0000 7.0000

-549.0000 -401.0000 -2.0000 196.0000

267.0000 195.0000 1.0000 -95.0000

-278.0000 -203.0000 -1.0000 99.0000

Solution for b

Using inverses function

A is not Invertible

Using MATLAB function inv()

Warning: Matrix is singular to working precision.

> In Run_inverse_func at 27

Inf Inf Inf Inf

Inf Inf Inf Inf

Inf Inf Inf Inf

Inf Inf Inf Inf

Solution for c

Using inverses function

-0.0049 0.0512 -0.0354 0.0012 0.0034

0.0431 -0.0373 -0.0046 0.0127 0.0015

-0.0303 0.0031 0.0031 0.0031 0.0364

0.0047 -0.0065 0.0108 0.0435 -0.0370

0.0028 0.0050 0.0415 -0.0450 0.0111

Using MATLAB function inv()

-0.0049 0.0512 -0.0354 0.0012 0.0034

0.0431 -0.0373 -0.0046 0.0127 0.0015

-0.0303 0.0031 0.0031 0.0031 0.0364

0.0047 -0.0065 0.0108 0.0435 -0.0370

0.0028 0.0050 0.0415 -0.0450 0.0111

Solution for d

Using inverses function

0 -0.1544 0.1838 0.0294

0 0.8162 -0.2574 -0.4412

0 -0.7206 0.1912 0.4706

1.0000 3.0000 -3.0000 -1.0000

Using MATLAB function inv()

Warning: Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.306145e-17.

> In Run_inverse_func at 45

1.0e+14 *

0.9382 2.8147 -2.8147 -0.9382

2.8147 8.4442 -8.4442 -2.8147

-2.8147 -8.4442 8.4442 2.8147

-0.9382 -2.8147 2.8147 0.9382

Explanation for different result in case of magic(4) :

The inv function fails if determinant of matrix is close to zero. Matrix is close to singular or badly scaled. Results may be inaccurate

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