Determinant and inverse of a 3 X 3 matrix Issue

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.

[Adam]

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

Answer 1

[Matt J]

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.

[Karan Kular]

In my code, I have included the cofactor calculations because I want to calculate the determinant and inverse of a 3 x 3 matrix not 2 x 2. If i use invandet2by2sol, this is just for 2 x 2 calculations of determinant and inverse, but the question wants 3 x 3 determinant and inverse, so i am confused on how to implement the function invanddet2by2sol in my code.

[Matt J]

As I said, each co-factor that you are currently computing explicitly can instead be obtained using invandet2by2sol. The co-factors are themselves just determinants of 2x2 matrices (up to a sign), which is what invandet2by2sol is designed to calculate. That is the reason I believe that invandet2by2sol was given to you.

[James Tursa]

@Karan: E.g.,

A11 = [(A(2,2) * A(3,3)) - (A(3,2) * A(2,3))];

can be rewritten as:

A11 = invanddet2by2sol( "a 2x2 matrix made up of appropriate matrix A parts" );

You just need to fill in the code for the appropriate 2x2 matrix.

[Karan Kular]

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]

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]

Yeah sorry silly mistake. Thanks for the tip.

Answer 2

[Massimo Zanetti]

You are getting this error because in your function

invanddet3by3(A)

there is NO CALL to function

invanddet2by2sol(...)

[Karan Kular]

Yes thank you, i have acknowledged this now but i am having a problem calling the invandet2by2sol function. Is it

function [ determinant, inverse] = invanddet3y3(invandet2by2sol(A));

[Massimo Zanetti]

In the method of cofactors for comptuting det of a 3x3 matrix, you need to compute det of 3 cofactors 2x2. Here it is a "tutorial"..

https://www.mathsisfun.com/algebra/matrix-inverse-minors-cofactors-adjugate.html

Invoke invandet2by2sol(..) for computing the 2x2 determinants.

If this answer heped you, please accept it.