P=matrix(c(1/4,1/4,1/4,1/4,1/5,1/5,2/5,1/5,1/3,1/3,1/6,1/6,1/6,1/3,1/3,1/6),nrow=4,ncol=4,byrow=T)

#### raising 25th power
y<-P
for(i in 1:24)
y<-y%*%P

### Solve the system of linear equations.
PP<-P-diag(4)
PP<-t(P-diag(4))
PP

for(i in 1:4)
PP[4,i]<-1
PP
solve(PP,c(0,0,0,1))

### Check eigen vector and eigen values

PPP<-t(P)
PPP
eigen(PPP)

### normalizing them
0.4824350/(0.4824350+0.5472064+0.5628408+0.3886282)
0.5472064/(0.4824350+0.5472064+0.5628408+0.3886282)
0.5628408/(0.4824350+0.5472064+0.5628408+0.3886282)
0.3886282/(0.4824350+0.5472064+0.5628408+0.3886282)