4327.sagews

P=matrix(QQ, 2, 2, [0.85, 0.1, 0.15, 0.9])
print P

[17/20 1/10] [ 3/20 9/10]

P.eigenvalues()

[1, 3/4]

D, S=P.eigenmatrix_right()
print D
print 
print S

[ 1 0] [ 0 3/4] [ 1 1] [3/2 -1]

S.inverse()*D*S

[17/20 1/10] [ 3/20 9/10]

S.inverse()

[ 2/5 2/5] [ 3/5 -2/5]

x=matrix(2, 1, [1000, 200])
print x

[1000] [ 200]

P^50*x.n()

[480.000294487261] [719.999705512739]