%% Create Matrices

% Create y (solution) vector
y(1)        = 80;
y(2:6)      = 40;
y(7:10)     =  0;
y(11)       = 40;
y(12:15)    =  0;
y(16)       = 40;
y(17:20)    =  0;
y(21)       = 30;
y(22:25)    = 10;

% Create diagonal vector for 4

for i = 1:25
    v(i) = 4;
end

% Create diagonal vector for -1 dependant on the sizes needed

for i = 1:24
    w(i) = -1;
end

for i = 1:20
    k(i) = -1;
end

% Create vector A with the diagonals

A = diag(v) + diag(w,1) + diag(w,-1) + diag(k,5) + diag(k,-5);

% Remove undependant variables from A (edges of the roster)

for i=5:5:19;
    j= i+1;
    A(j,i) = 0;
    i+5;
end

% Solve for 'x'

x = A\y';

%% Plot the solution

% Create matrix X to correspond to the grid
s = 1
for i = 1:5
    for j = 1:5
        X(i,j) = x(s);
        s = s+1;
    end
end

% Plot X with surf

surf(X);