How to use a solver function to solve matrix?

So I have an equation that goes something like N.*P + S.*P + E.*P + W.*P = Q N S E and W are coefficients, P is pressure changing with time. In terms of [A]*[x]=[b] its supposedly [coefficients]*[Pressure]=[Q]. How would I use a solver to translate the equation into these matrix terms?

[zephyr21]

Another way to phrase my question, how would I populate the A,x, and b matrices?

Answer 1

[Ayush]

Hi @zephyr21

The matrix form [A]*[x]=[b] translates to:

• [A] is the matrix of coefficients.
• [x] is the vector of unknowns (in your case, the pressure P).
• [b] is the vector of constants (in your case, Q).

Assuming you have multiple such equations, you would set them up as follows:

1. Define the coefficients matrix [A]: Each row represents the coefficients of a single equation.
2. Define the vector [b]: Each element represents the right-hand side of an equation.
3. Solve for [x]: Use MATLAB's matrix division or other solvers to find [x].

% Define the coefficients matrix [A]
% Each row corresponds to one equation
A = [
    N1 + S1 + E1 + W1;
    N2 + S2 + E2 + W2;
    N3 + S3 + E3 + W3;
    % Add more equations as needed
];

% Define the vector [b]
% Each element corresponds to the Q value of an equation
b = [
    Q1;
    Q2;
    Q3;
    % Add more Q values as needed
];

% Solve for [x] using the backslash operator
% This finds the vector of pressures [P]
x = A \ b;

% Display the result
disp('The pressures P are:');
disp(x);

I hope it helps!