How to Concatenate Matrix in MATLAB?

Question: How to generate the following matrix in MATLAB?

$$\left[\begin{array}{cccccccccc}1& 0& 0& 0& 0& 0& 0& 0& 0& 0\\ 0& 3& 0& 0& 0& 2& 4& 6& 8& 10\\ 0& 0& 5& 0& 0& 12& 14& 16& 18& 20\\ 0& 0& 0& 7& 0& 22& 24& 26& 28& 30\\ 0& 0& 0& 0& 11& 0& 0& 0& 0& 0\\ 0& 0& 0& 0& 0& 13& 0& 0& 0& 0\\ 3& 3& 3& 3& 0& 0& 17& 0& 0& 0\\ 3& 2& 2& 3& 0& 0& 0& 19& 0& 0\\ 3& 2& 3& 3& 0& 0& 0& 0& 23& 0\\ 3& 3& 3& 3& 0& 0& 0& 0& 0& 29\end{array}\right]$$

Answer:

1. The above matrix can easily be generate by first defining a zero matrix $A$ of $n\times n$ (in our case it's $10$).
2. Then create arrays of even numbers and store them in $B$.
3. Similarly generate $4\times 4$ of $3^{\prime }s$ matrix $C$
4. Replace few elements according to the given condition.
5. Now, first generate prime numbers on the diagonal
6. Now substitute (technically concatenate) these smaller size matrices in the bigger matrix $A$ by specfiying the rows and columns.

Below is the code that follows all the steps mentioned above

clear all; clc; close all;
A = zeros(10);
B2 = 2:2:10;
B3 = B2 + 10;
B4 = B3 +10;
B = [B2;B3;B4];
C = 3*ones(4);
C(2,2:3) = 2;
C(3,2)  = 2;
A = diag(primes(29));
A(2:4,6:10) = B;
A(7:10,1:4) = C;
disp(A)

Output:

     2     0     0     0     0     0     0     0     0     0
     0     3     0     0     0     2     4     6     8    10
     0     0     5     0     0    12    14    16    18    20
     0     0     0     7     0    22    24    26    28    30
     0     0     0     0    11     0     0     0     0     0
     0     0     0     0     0    13     0     0     0     0
     3     3     3     3     0     0    17     0     0     0
     3     2     2     3     0     0     0    19     0     0
     3     2     3     3     0     0     0     0    23     0
     3     3     3     3     0     0     0     0     0    29

Useful MATLAB built-in commands

• zeros --- Create array of all zeros
• ones --- Create array of all ones
• diag --- Create diagonal matrix or get diagonal elements of matrix
• eye --- Identity matrix
• cat --- Concatenate arrays
• horzcat --- Concatenate arrays horizontally
• vertcat --- Concatenate arrays vertically

Enjoy Learning Simple things, as learning never stops. Thanks for reading!