Matrix calculus and solving system of equations

I have a Aleator.xlsx table from I imported the integer value in D => and construct a matrix in the first column we write the difference

DM(i,1) = D(i,1)-D(i+1,1); .... DM(i,10) = D(i,10)-D(i+1,10); and b1= D(1027,1).. b10= D(1017,1);

I have to calculus the coeficents a11, ...a10,1 from equations

b1 = DM(1,1)*a11+DM(1,2)*a21+DM(1,3)*a31+DM(1,4)*a41+DM(1,5)*a51+DM(1,6)*a61+DM(1,7)*a71+DM(1,8)*a81+DM(1,9)*a91+DM(1,10)*a101;

b10 = DM(10,1)*a11+DM(10,2)*a21+DM(10,3)*a31+DM(10,4)*a41+DM(10,5)*a51+DM(10,6)*a61+DM(10,7)*a71+DM(10,8)*a81+DM(10,9)*a91+DM(10,10)*a101;

And write the result in Vector Rez = [a11 a21 ... a101];

Please Help!

Answer 1

[Jaimin]

Hi @Viorel-Mihai Popescu

From the description, I understand there is a file named 'Aleator.xlsx' that contains the necessary data. You want to use this data to solve a system of linear equations.

We can use the “readmatrix” function to load the data, and the "\" operator to solve the system of linear equations.

Here I have attached sample code for better understanding.

% Step 1: Load the Excel file
filePath = 'Aleator.xlsx'; % Replace with your actual file path
data = readmatrix(filePath);

% Step 2: Extract the integer values from column D
D = data(:, 4); % Assuming column D is the 4th column

% Step 3: Construct the difference matrix DM
DM = zeros(10, 10);
for i = 1:10
    DM(i, :) = D(i) - D(i+1:i+10);
end

% Step 4: Extract b1 to b10
b = [D(1027); D(1026); D(1025); D(1024); D(1023); D(1022); D(1021); D(1020); D(1019); D(1018)];

% Step 5: Solve the system of equations
% DM' * a = b
a = DM' \ b; % Transpose DM to match the equation format

% Step 6: Write the result in Vector Rez
Rez = a;

% Display the result
disp('Vector Rez =');
disp(Rez);

For more information on the 'readmatrix' function, please refer to the MathWorks documentation.

readmatrix:

https://www.mathworks.com/help/matlab/ref/readmatrix.html

For more information on system of linear equation, please refer to the MathWorks documentation.

Systems of Linear Equations:

https://www.mathworks.com/help/matlab/math/systems-of-linear-equations.html

I hope this will be helpful.

Answer 2

[Dheeraj]

Hi Viorel-Mihai Popescu,

You can use "xlsread" function to read to the file and the data associated with it. you need to set up a system of linear equations based on the provided matrix equations and solve for the coefficients . Below is an example to do the same assuming you have "DM" matrix created using your logic.

Formulate the system of equations
% We need to solve DM * a = b
% DM is (nRows - 1) x nCols matrix
% b is a column vector of size nCols

% Check if we have enough equations and variables
if size(DM, 1) < nCols
    error('Insufficient number of equations.');
end

% Solve for coefficients a
% We are solving DM * a = b
% Using left division to find a
a = DM \ b;

Thank You.

[Viorel-Mihai Popescu]

Error using \

Matrix dimensions must agree.

Error in DMem (line 60)

a = DM \ b;

It doesn't work

[Torsten]

Insert the lines

size(DM)
size(b)

before using the command

a = DM \ b;

What does MATLAB print out for the two sizes ?

[Viorel-Mihai Popescu]

Now has no compile error but have some logical emprovement...