How can I easily plot a system of linear equations?

I would like to quickly plot a vector field of a system of first-order linear equations, for example:

Which I made using:

clear,clc

A = [1,  1;
     4,  1;]
    
[x1,x2]=meshgrid(-2:0.2:2,-2:0.2:2);
x1=flip(x1);
x1dot=zeros(length(x1),length(x2));
x2dot=x1dot;


 for i=1:length(x1)
    for j=1:length(x2)
        x1dot(i,j) = A(1,1)*x1(1,i) + A(1,2)*x2(j,1);
        x2dot(i,j) = A(2,1)*x1(1,i) + A(2,2)*x2(j,1);
    end
 end
 
x1dotn= x1dot./sqrt(x1dot.^2+x2dot.^2);
x2dotn= x2dot./sqrt(x1dot.^2+x2dot.^2);

quiver(x2,x1,x1dotn,x2dotn);

This works fine, however I feel like this is quite cumbersome and could be done more elegantly and easier? Perhaps there is even a function for it I missed?

Answer 1

[Harshit Jain]

Since you are using only the first row of x1 and first column of x2, you can vectorize this implementation.

Steps which you can do.

1. Get first row of x1.
2. Get first column of x2.
3. Make A into row vector.
4. Make a new vector from row of x1 and column of x2.
5. Do element wise multiplication to get result.

These are not exact steps but a rough idea so that you can use this to solve the problem.

Refer to this link to find more information about how to vectorize.