Exercise C11

library(pracma)
A = matrix(c(3,0,1,2,1,2,1,1,0),ncol = 3)
A
##      [,1] [,2] [,3]
## [1,]    3    2    1
## [2,]    0    1    1
## [3,]    1    2    0
eigen_A <- eigen(A)
eigen_A$values # Eigen values
## [1]  3.618034  1.381966 -1.000000

\[ \lambda = 3.6180, \lambda = 1.3819, \lambda = -1 \]

charpoly(A) # Characteristic polynomial
## [1]  1 -4  0  5

\[ p(\lambda) = \lambda^3 - 4\lambda^2 + 5 = 0 \]