Growing Diagonal Matrix Problem

I am trying to create a diagonal matrix that can grow a # of rows and # of collumns. These collumns can be from a range of 10 to 100000 to infinite but must maintain a pattern.

For simplicity I am using a 9x9 Matrix. It seems like it is repeating 3 matrics over and over.

1 - Diagonal

1 - Ones Diagonal

1 - Zeros

A B 0 1 0 0 0 0 0

B A B 0 1 0 0 0 0

0 B A 0 0 1 0 0 0

1 0 0 A B 0 1 0 0

0 1 0 B A B 0 1 0

0 0 1 0 B A 0 0 1

0 0 0 1 0 0 A B 0

0 0 0 0 1 0 B A B

0 0 0 0 0 1 0 B A

I am having a hard time trying to seeing how to write this.

Answer 1

[Matt J]

A=3; B=4;
M=[A B 0; B A B; 0 B A]; 

n=3;

e = ones(n,1);
Q = spdiags([e 0*e e],-1:1,n,n);
%Q=toeplitz(sparse([0,1,zeros(1,n-2)]));
result =kron(speye(n),M)+kron(Q,eye(3));

full(result)

ans = 9×9

3 4 0 1 0 0 0 0 0 4 3 4 0 1 0 0 0 0 0 4 3 0 0 1 0 0 0 1 0 0 3 4 0 1 0 0 0 1 0 4 3 4 0 1 0 0 0 1 0 4 3 0 0 1 0 0 0 1 0 0 3 4 0 0 0 0 0 1 0 4 3 4 0 0 0 0 0 1 0 4 3

[WARRIOR24]

I need the big matix to be changable, like if the 9x9 can be change to a 100x100. The 9x9 is just an example.

[Matt J]

I know it's just an example. So is the value of n=3 in my code.

[WARRIOR24]

Here is my next problem, what is it need to be changed to 8x8? But keep everything the same except the last row and collumn?

[Matt J]

If you mean you want to remove the last row and column, then,

result(:,end)=[]; %remove last column
result(end,:)=[]; %remove last row