How do I make a function work?

function Kram=linsolve (A,B)

[m,n]=size(A);
x=zeros(m,1);

for i=1:m
    Ad = A;%Додаткова матриця;
    Ad(:,i) = B;
    xd = det(Ad) / det(A);%Корінь рівняння;
    x(i,1)=xd;%Вектор коренів;
    
end

end

This function solves the problem of roots in this way:

A=randn(2), B=rand(2,1), Kram=linsolve (A,B)

A =

-0.9606 0.7612

-1.6338 1.1933

B =

0.9345

0.1079

Kram =

10.6159

14.6250

However, it doesn´t do the solution checking right:

x_r=x

x_r =

Columns 1 through 10

-4.5000 -4.2374 -3.9747 -3.7121 -3.4495 -3.1869 -2.9242 -2.6616 -2.3990 -2.1364

Columns 11 through 20

-1.8737 -1.6111 -1.3485 -1.0859 -0.8232 -0.5606 -0.2980 -0.0354 0.2273 0.4899

Columns 21 through 30

0.7525 1.0152 1.2778 1.5404 1.8030 2.0657 2.3283 2.5909 2.8535 3.1162

Columns 31 through 40

3.3788 3.6414 3.9040 4.1667 4.4293 4.6919 4.9545 5.2172 5.4798 5.7424

Columns 41 through 50

6.0051 6.2677 6.5303 6.7929 7.0556 7.3182 7.5808 7.8434 8.1061 8.3687

Columns 51 through 60

8.6313 8.8939 9.1566 9.4192 9.6818 9.9444 10.2071 10.4697 10.7323 10.9949

Columns 61 through 70

11.2576 11.5202 11.7828 12.0455 12.3081 12.5707 12.8333 13.0960 13.3586 13.6212

Columns 71 through 80

13.8838 14.1465 14.4091 14.6717 14.9343 15.1970 15.4596 15.7222 15.9848 16.2475

Columns 81 through 90

16.5101 16.7727 17.0354 17.2980 17.5606 17.8232 18.0859 18.3485 18.6111 18.8737

Columns 91 through 100

19.1364 19.3990 19.6616 19.9242 20.1869 20.4495 20.7121 20.9747 21.2374 21.5000

>> F=A*x_r-B

Error using *

Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix

matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'.

Related documentation

What should I do?

Answer 1

[Voss]

Your function returns a variable called Kram, but no variable with that name is calculated within the function.

I assume you want to return what you call x in the function.

format long g

A=randn(2), B=rand(2,1)

A = 2×2

-0.0823460205646498 -2.21863794181447 1.6232134952347 1.04101266770237

B = 2×1

0.120008128513305 0.0050788186937395

x_r = lin_solve(A,B)

x_r = 2×1

0.0387410540739482 -0.0555287989206656

F=A*x_r-B

F = 2×1

1.0e+00 * 1.38777878078145e-17 6.93889390390723e-18

function x=lin_solve(A,B)
[m,n]=size(A);
x=zeros(m,1);
for i=1:m
    Ad = A;%Додаткова матриця;
    Ad(:,i) = B;
    xd = det(Ad) / det(A);%Корінь рівняння;
    x(i,1)=xd;%Вектор коренів;
end
end

[Alisa-Oleksandra Kotliarova]

Thank you so much, that helped a lot!

[Voss]

You're welcome!

Answer 2

[Sulaymon Eshkabilov]

There are a couple of critical points:

(1) Don't use MATLAB's builtin fucntion names for your own functions that corrupts MATLAB fcns, i.e.:

% function Kram= lin_solve(A,B); % instead of linsolve (A,B)
% [m,n]=size(A);
% x=zeros(m,1);
% ...
% end

(2) It is not clear what you are try to do here inside the above fcn:

%     for i=1:m
% Ad = A;%Додаткова матриця;
% Ad(:,i) = B;
% xd = det(Ad) / det(A);%Корінь рівняння;
% x(i,1)=xd;%Вектор коренів;
%     end   

(3) If you want to verify the found solution and compute the error. It can be done in this way, i.e.:

A=randn(2); B=rand(2,1); X_Sol=linsolve(A,B); 
Error = norm(A*X_Sol-B)/norm(B)

Error = 0

(4) If you have many sets of equations and want to verify their solutions, it can be simulated something like this way:

for ii = 1:10
    rng(ii)
    A=randn(2); B=rand(2,1);    
    X_Sol(:,ii)=linsolve(A,B);  % store solutions if necessary
    Error = norm(A*X_Sol(:,ii)-B)/norm(B)
end

Error = 7.0704e-17

Error = 1.0383e-16

Error = 8.7752e-17

Error = 3.7999e-17

Error = 3.1714e-16

Error = 0

Error = 1.9889e-16

Error = 0

Error = 0

Error = 1.0151e-16

[Alisa-Oleksandra Kotliarova]

Thanks a lot, that`s quite useful!