Determinant and inverse of a 3 X 3 matrix Issue

Question

Karan Kular 2016-10-26

0
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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/309295-determinant-and-inverse-of-a-3-x-3-matrix-issue

评论： Karan Kular 2016-10-27

Hi I have a question:

I need to create a function that calculates the determinant and the inverse of a generic 3 X 3 matrix with the method of the cofactors and the adjoint matrix.

The function should be named invanddet3by3. The function takes a generic 3 X 3 matrix as input, and returns two outputs: the determinant and the inverse. It should do the following few things:

It calculates the determinant using the cofactors.

If the determinant is zero, the inverse is set to be an empty matrix ([])

If the determinant is non-zero, then it calculates the inverse.

However I MUST USE THE FUNCTION invanddet2by2sol provided to me which is :

function [ determinant, inverse ] = invanddet2by2sol( A )
% INVANDDET2BY2 Calculates the determinant and the inverse of a 2 X 2 matrix
determinant = A(1,1)*A(2,2)- A(1,2)* A(2,1); % calculates the determinant
if determinant ==0 % if the matrix is singular
    inverse = []; % inverse does not exist
else    
    inverse = [A(2,2)  -A(1,2); -A(2,1) A(1,1)]./determinant; % calculates the inverse
end

Here is my attempt :

function [determinant , inverse ] = invanddet3by3(A)
%INVANDDET3BY3 Calculates the determinant and the inverse of a 3 X 3 matrix by using
% cofactors and adjoint matrix
A11 = [(A(2,2) * A(3,3)) - (A(3,2) * A(2,3))]; % Cofactors 3x3 matrix A
A12 = - [(A(2,1) * A(3,3)) - (A(3,1) * A(2,3))];
A13 = [(A(2,1) * A(3,2)) - (A(3,1) * A(2,2))];
A21 = - [(A(1,2) * A(3,3)) - (A(3,2) * A(1,3))];
A22 = [(A(1,1) * A(3,3)) - (A(3,1) * A(1,3))];
A23 = - [(A(1,1) * A(3,2)) - (A(3,1) * A(1,2))];
A31 = [(A(1,2) * A(2,3)) - (A(2,2) * A(1,3))];
A32 = - [(A(1,1) * A(2,3)) - (A(2,1) * A(1,3))];
A33 = [(A(1,1) * A(2,2)) - (A(2,1) * A(1,2))];
J = [ A11 A12 A13; A21 A22 A23; A31 A32 A33]; % Adjugate Matrix
determinant = ((A(1,1) * A11) + (A(1,2) * A12) + (A(1,3) * A13)); % Determinant of A
inverse = (1/determinant) * (J'); % Inverse of A
if determinant==0
inverse=[];
end
end

My code passes all the tests for calculating the determinant and inverse correctly, but its saying: 'The submission must contain the following functions or keywords: invanddet2by2sol You MUST use the function invanddet2by2sol!'.

I have tried many things but have been unsuccessful.

Would appreciate the help,

Thanks very much.

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Adam 2016-10-26

Is one of the things that you have tried using the function provided to you that you MUST use?!

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Answer 1

Matt J 2016-10-26

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/309295-determinant-and-inverse-of-a-3-x-3-matrix-issue#answer_240869

编辑：Matt J 2016-10-26

在 MATLAB Online 中打开

In the code that you have provided, your cofactor calculations in fact consist of many 2x2 determinant calculations

    A11 = [(A(2,2) * A(3,3)) - (A(3,2) * A(2,3))]; % Cofactors 3x3 matrix A
    A12 = - [(A(2,1) * A(3,3)) - (A(3,1) * A(2,3))];
    A13 = [(A(2,1) * A(3,2)) - (A(3,1) * A(2,2))];
    etc...

You are probably intended to use invandet2by2sol to do these 2x2 determinant calculations.

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Karan Kular 2016-10-27

在 MATLAB Online 中打开

I have amended my code, but now i am failing a different test.

Here is my new code:

function [determinant , inverse ] = invanddet3by3(A)
%INVANDDET3BY3 Calculates the determinant and the inverse of a 3 X 3 matrix by using cofactors and adjoint matrix
    A11 = invanddet2bysol([A(2,2), A(2,3); A(3,2), A(3,3)]); % Cofactors 3x3 matrix A
    A12 = -(invanddet2by2sol([A(2,1), A(2,3); A(3,1), A(3,3)]));
    A13 = invanddet2by2sol([A(2,1), A(2,2); A(3,1), A(3,2)]);
    A21 = -(invanddet2by2sol([A(1,2), A(1,3); A(3,2), A(3,3)]));
    A22 = invanddet2by2sol([A(1,1), A(1,3); A(3,1), A(3,3)]);
    A23 = -(invanddet2by2sol([A(1,1), A(1,2); A(3,1), A(3,2)]));
    A31 = invanddet2by2sol([A(1,2), A(1,3); A(2,2), A(2,3)]);
    A32 = -(invanddet2by2sol([A(1,1), A(1,3); A(2,1), A(2,3)]));
    A33 = invanddet2by2sol([A(1,1), A(1,2); A(2,1), A(2,2)]);
    J = [ A11 A12 A13; A21 A22 A23; A31 A32 A33]; % Adjugate Matrix
    determinant = ((A(1,1) * A11) + (A(1,2) * A12) + (A(1,3) * A13)); % Determinant of A
    inverse = (1/determinant) * (J'); % Inverse of A
if determinant==0
    inverse=[];
end
end

New error : Undefined function 'invanddet2bysol' for input arguments of type 'double'.

Error in invanddet3by3 (line 5) A11 = invanddet2bysol([A(2,2), A(2,3); A(3,2), A(3,3)]); % Cofactors 3x3 matrix A

Adam 2016-10-27

Surely it is obvious what the problem is there?! You have to get into the habit of rereading your code to find basic errors and you need o get used to reading the error message and interpreting it. Usually the errors are exactly as they say.

Karan Kular 2016-10-27