library (pracma)
## Warning: package 'pracma' was built under R version 4.2.2
Sample <- matrix( c( 1, 2, 3, 0, 4, 5, 0, 0, 6 ), nrow=3, byrow=TRUE )

Let’s Calculate the Eigenvalues 

eigenValue <- eigen(Sample)
eigenValue$values
## [1] 6 4 1

The Eigenvalues are 6, 4, and 1

Now Let’s Calculate the Eigenvectors 

eigenValue$vectors
##           [,1]      [,2] [,3]
## [1,] 0.5108407 0.5547002    1
## [2,] 0.7981886 0.8320503    0
## [3,] 0.3192754 0.0000000    0

Finally, lets calculate the polynomial equation 

polynomial = charpoly(Sample)
polynomial
## [1]   1 -11  34 -24

The characteristic polynomial is:

X3-11x2+34x-24