Jennings (1977, p. 244) gave the following (transpose of ) transition matrix (n = 7) for a Markov chain: diagonals (Aii) are .9, .6, .7, .6, .7, .7, .8; superdiagonals (Ai,i+1) are .3, .2, .3, .2, .3,...

Jennings (1977, p. 244) gave the following (transpose of ) transition matrix (n = 7) for a Markov chain:

diagonals (Aii) are .9, .6, .7, .6, .7, .7, .8;

superdiagonals (Ai,i+1) are .3, .2, .3, .2, .3, .2;

second subdiagonal (Ai+2,i) are all .1.

Write code to multiply any vector x by this transition matrix A, exploiting its banded structure.