Code:
A = [1/3 1/4 0;1/3 1/2 1;1/3 1/4 0]
B = A^100
C = rats(B)
Output:
A =
0.3333
0.2500 0
0.3333
0.5000 1.0000
0.3333
0.2500 0
B =
0.2143
0.2143 0.2143
0.5714
0.5714 0.5714
0.2143
0.2143 0.2143
C =
3×42 char array
'
3/14
3/14
3/14 '
'
4/7
4/7
4/7 '
'
3/14
3/14
3/14 '
C gives you the P^100 in exact rational form.
Also by eigenvalue decomposition note that the steady-state vector is (3,8,3)^t.
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