4326.sagews

P=matrix(QQ, 2, 2, [0.75, 0.05, 0.25, 0.95])
print P

[ 3/4 1/20] [ 1/4 19/20]

P.eigenvalues()

[1, 7/10]

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

[ 1 0] [ 0 7/10] [ 1 1] [ 5 -1]

S.inverse()*D*S

[ 3/4 1/20] [ 1/4 19/20]

S.inverse()

[ 1/6 1/6] [ 5/6 -1/6]

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

[1000] [ 200]

P^50*x.n()

[200.000014387720] [999.999985612280]