How is dimensions of transformation matrix k is coming?

#1

At first it is k1 now at 13:30 it is 33;

#2

the dimension of transformation matrix depends on the number of terms the recurrence is depended upon-
ex fibonacci sequence f(n) depends on f(n-1) and f(n-2) so , k=22.
ex- if sequence depends on previuous 3 terms then it will be 44. etc