C11 Find the characteristic polynomial of the matrix A

\[\mathbf{A} = \left[\begin{array} {rrr} 3 & 2 & 1 \\ 0 & 1 & 1 \\ 1 & 2 & 0 \end{array}\right]\]

Now solving for the determinant of \[A-\lambda*I=0\]

\[\mathbf \det \left[\begin{array} {rrr} \lambda-3 & 2 & 1 \\ 0 & \lambda-1 & 1 \\ 1 & 2 & \lambda-0 \end{array}\right]\]

A <- matrix(c(3,2,1,
              0,1,1,
              1,2,0), 3, byrow=T)

print(A)
##      [,1] [,2] [,3]
## [1,]    3    2    1
## [2,]    0    1    1
## [3,]    1    2    0
library(pracma)
rref(A)
##      [,1] [,2] [,3]
## [1,]    1    0    0
## [2,]    0    1    0
## [3,]    0    0    1
Rank(A)
## [1] 3
charpoly(A)
## [1]  1 -4  0  5