Matrix is singular to working precision.

I'm getting the error "Matrix is singular to working precision." I'm not sure what is wrong with my code but I need to not get zeros for my Total Stiffness Matrix, Nodal Forces, and Nodal Dispalcements. What should I do?

E = 200e9 * ones(2,1);
L = 2 * ones(2,1);
I = 3e-4 * ones(2,1);
kb = E.*I./L.^3;
q = 2e3; %---Positive for -y direction
f0 = q*[-L(2)/2;-L(2)^2/12;-L(2)/2;L(2)^2/12];
K = beam_stiffness(kb,L);
K(4:6,4:6)

ans = 3x3

0 0 0 0 0 0 0 0 0

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d_part = K(4:6,4:6)\f0(2:end);

Warning: Matrix is singular to working precision.

d = [0;0;0;d_part];
f_eff = K * d;
f = f_eff - [0;0;-q*L(2)/2;-q*L(2)^2/12;-q*L(2)/2;q*L(2)^2/12];
t = zeros(size(L));
for cnt=1:length(L)
    n{cnt} (1) = cnt;
    n{cnt} (2) = cnt + 1;
end


function result = beam_stiffness(kb,l)
if ~(length(kb)==length(l))
    error('Base stiffness and length arrays must have equal number of elements.');
end
num_elem = length(kb);
num_node = num_elem + 1;
ke = zeros(4,4,length(kb));
for cnt=1:num_elem
    ke(:,:,cnt) = kb(cnt) * [12 6*l(cnt) -12 6*l(cnt);
        6*l(cnt) 4*l(cnt)^2 -6*l(cnt) 2*l(cnt)^2;
        -12 -6*l(cnt) 12 -6*l(cnt);
        6*l(cnt) 2*l(cnt)^2 -6*l(cnt) 4*l(cnt)^2];
end
K = zeros(2*num_node,2*num_node);
for cnt=1:num_elem
    K(2*cnt-1:2*cnt+2,2*cnt-1:2*cnt+2) - K(2*cnt-1:2*cnt+2,2*cnt-1:2*cnt+2) + ...
        ke(:,:,cnt);
end
result = K;
end

Answer 1

[Torsten]

Obviously, your matrix is the zero matrix.

Most probably the reason is that you don't assign values to K in the loop

K(2*cnt-1:2*cnt+2,2*cnt-1:2*cnt+2) - K(2*cnt-1:2*cnt+2,2*cnt-1:2*cnt+2) + ...
    ke(:,:,cnt);