MATLAB: Am I getting the error: “Error using + Matrix dimensions must agree.”

error using *forglobal stiffness matrixloopmatrix dimensions must agree

Hello,
I am trying to create a 21×21 global stiffness matrix that look like this:
K = [1 -1  0  0  0...;
    -1  2 -1  0  0...;
     0 -1  2 -1  0...;
     0  0 -1  2 -1...
     ...]
This is my code so far:
 % Define number of nodes
 N = 21;
 k1 = [1 -1; -1 1];
 % Define global stiffness matrix with zeros
 K = zeros(N);
 % Populate diagonal of matrix, making sparse matrix
 for i = 1:(N-1)
    for j = 2:N
        K(i:j,i:j) = K(i:j,i:j) + k1
    end
 end
However, I am getting error:
 Error using  + 
 Matrix dimensions must agree.
 Error in Untitled2 (line 16)
        K(i:j,i:j) = K(i:j,i:j) + k1
The dimensions of the matrices that are being added are both 2×2 in every iteration so I do not understand why the loop stops after the first iteration. Any suggestions?
I have written the code for each iteration manually just to double check and the I end up with the correct solution. However, I want to know why the for loop solution is not working. Here is the code for the manual iterations:
 K(1:2,1:2) = K(1:2,1:2) +k1
 K(2:3,2:3) = K(2:3,2:3) +k1
 K(3:4,3:4) = K(3:4,3:4) +k1
 K(4:5,4:5) = K(4:5,4:5) +k1
 K(5:6,5:6) = K(5:6,5:6) +k1
 ....
I appreciate the help in advance.

Best Answer

I realized that I misunderstood the the nested for loop for a little while. I ended up figuring it out with a single for loop. For those that are curious and need help with a similar problem, this is my code. I'm sure this is a very inefficient way to solve the problem but its simple enough for me to understand as I am a beginner.
 % Define number of nodes
 N = 21;
 % Define global stiffness matrix with zeros
 K = zeros(N);
 % Define local stiffness matrix
 k1 = [1 -1; -1 1];
 % Populate diagonal of global stiffness matrix
 for i = 1:N-1
    K(i:i+1,i:i+1) = K(i:i+1,i:i+1) + k1;
 end
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