Solve a system of linear equations in matrix form

I want to solve the following system of linear equations.

u1 - u2 = 11.1680

u1 - u4 = 22.8197

u3 - u5 = 8.7093

u5 - u1 = 0.3391

u5 - u2 = 11.4875

So I want to create 2 matrices and set them equal to each other and simply solve them in matrix form.

So here's what I've done:

u=sym('u%d',[5,1]);                                     % u=[u1 ; u2 ; u3 ; u4 ; u5]
Left    =    [u1-u2 ; u1-u4 ; u3-u5 ; u5-u1 ; u5-u2];   % Left side of the above equation system
Right   =    [11.1680 ; 22.8197 ; 8.7093 ; 0.3391 ; 11.4875];    % Right side of the above equation system
solve(Left==Right)

but what MATLAB returns is this:

ans = 

  struct with fields:

    u1: [0×1 sym]
    u2: [0×1 sym]
    u3: [0×1 sym]
    u4: [0×1 sym]
    u5: [0×1 sym]

What is the problem?

Has anyone any idea how I can solve these equations in matrix form?

Answer 1

[Star Strider]

The problem is that the system is sparse, so you need to use sparse functions with it.

Try this:

Left = [1 -1 0 0 0; 1 0 0 -1 0; 0 0 1 0 -1; -1 0 0 0 1; 0 -1 0 0 1];
u = lsqr(Left,Right)

producing:

u =
   -0.0644
   -0.3004
    1.9476
   -2.1104
    0.5276