Creating a matrix that calculates inverse and determinants without using the det and inv commands

Hi, i have the following question:

Create a function that calculates the determinant and the inverse of a generic 2 X 2 matrix

The function should be named invanddet2by2. The function takes a generic 2 X 2 matrix as input, and returns two outputs: the determinant and the inverse. It should do the following few things:

It calculates the determinant

If the determinant is zero, the inverse is set to be an empty matrix (i.e. you assign the value [], that's squared brackets with no values inside, which for Matlab means an empty matrix)

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

So far i have

M=[ 4 5;6 9]
d_correct=(M(1,1)*M(2,2))-(M(1,2)*M(2,1))
if d_correct==0
B=[0 0; 0 0]
else
Diagonal=[9 -5;-6 4]
Minv_correct=d_correct *(1./M)
'end'

and my codes fail the test for the inverse of the singular matrix and for the determinant of the singular matrix

Does anyone have an idea of what's gooing wrong?

[Chaya N]

This code should not even be running, owing to the fact that an 'end' statement is missing!

[Rafaela Stylianou]

it's a typo i actually have included the 'end'

[Jan]

@Rafaela: Then please insert it in the question also.

Answer 1

[James Tursa]

Create a file in your working directory called invanddet2by2.m, e.g.

edit invanddet2by2.m

In that file, put the following function code (some function wrapper code with your code inside):

% Insert comments here describing function purpose, inputs, and outputs
function [B,d_correct] = invanddet2by2(M)
d_correct = (M(1,1)*M(2,2))-(M(1,2)*M(2,1));
if d_correct==0
    B = [0 0; 0 0];  <-- Fix this line to return the empty matrix [] instead of a 0's matrix
else
    Diagonal = [9 -5;-6 4];  <-- Fix this line to be a generic formula of M elements, not hard-coded values
    Minv_correct = d_correct *(1./M);  <-- Fix this line to use Diagonal, do the division in the correct order, and assign to B
end

Make changes and corrections to the lines that I have indicated.

[Rafaela Stylianou]

Thank you!

[Tai Lopez]

I'm having a similar problem. so I've created a function, it works when I type any 2x2 matrix but it doesn't run. do you know what is wrong with it? I've also attached a picture which shows the error. This is what I have:

function [Inverse, Determinant] = invanddet2by2(M)
% INVANDDET2BY2 Calculates the determinant and the inverse of a 2 X 2 matrix.
% It calculates the determinant.
% 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
Determinant = (M(1,1)*M(2,2))-(M(1,2)*M(2,1))

if Determinant==0
    Inverse = [];
else
     Madj_correct = trace(M)*eye(size(M)) -

[Steven Lord]

You call your function with 0 input arguments. MATLAB doesn't know what it should use as the M matrix in your function. Call it and pass your matrix in as the input.

Answer 2

[Chaya N]

A singular matrix, by definition, is one whose determinant is zero. hence, it is non-invertible. In code, this would be represented by an empty matrix. Therefore (using the same variable name as in your code),

 B = [];

For a non-singular matrix M, recall that M * inverse(M) = I, the identity matrix. This is the simplest expression you could use to generate your inverse matrix. Therefore,

 Minv_correct = eye(size(M))/M; % Note that this is regular division, NOT element-wise operation

There is also another commonly used method, that involves the adjoint of a matrix and the determinant to compute the inverse as inverse(M) = adjoint(M)/determinant(M). This involves the additional step of computing the adjoint matrix. For a 2 x 2 matrix, this would be computed as adjoint(M) = trace(M)*I - M. Therefore,

 Madj_correct = trace(M)*eye(size(M)) - M;
 Minv_correct = Madj_correct/d_correct;

You could use either of the above methods to compute your inverse matrix.

Answer 3

[Walter Roberson]

In the case of the determinant being 0, you are not setting the inverse to the empty matrix.

You are not using the variable Diagonal .

Your formula for obtaining the inverse from the determinant is incorrect. See https://en.wikipedia.org/wiki/Invertible_matrix#Analytic_solution