CUNY 605 Discussion Week 3

Discussion Week 3

Find the characteristic polynomial of the matrix A

\[A = \begin{pmatrix}3&2&1\\ 0&1&1\\ 1&2&0 \end{pmatrix}\]

\[\lambda = \begin{pmatrix}1&0&0\\ 0&1&0\\ 0&0&1 \end{pmatrix}\]

\[(\lambda I-A) = \begin{pmatrix}\lambda-3&2&1\\ 0&\lambda-1&1\\ 1&2&\lambda-0 \end{pmatrix}\]

\[det \begin{pmatrix}\lambda-3&2&1\\ 0&\lambda-1&1\\ 1&2&\lambda-0 \end{pmatrix}\]

In R, using the pracma library

library(pracma)

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

##      [,1] [,2] [,3]
## [1,]    3    2    1
## [2,]    0    1    1
## [3,]    1    2    0

charpoly(A, info = FALSE)

## [1]  1 -4  0  5