Question C10 P 388

Find the characteristic polynomial of the matrix A =1 2 3 4.

Using charpoly function to find the polynomial matrix

# create the matrix
A <- matrix(c(1,2,3,4), nrow = 2, byrow = TRUE)
A
##      [,1] [,2]
## [1,]    1    2
## [2,]    3    4
install.packages('pracma', repos = "http://cran.us.r-project.org")
## Installing package into 'C:/Users/Anil Akyildirim/Documents/R/win-library/3.6'
## (as 'lib' is unspecified)
## package 'pracma' successfully unpacked and MD5 sums checked
## 
## The downloaded binary packages are in
##  C:\Users\Anil Akyildirim\AppData\Local\Temp\Rtmpq4w4wC\downloaded_packages
library('pracma')
# use charpoly
charpoly(A, info = FALSE)
## [1]  1 -5 -2

The answer is:

\[t^{2} -5t -2 =0\]

Another Method to find the characteristic polynomial of matrix A

I <- matrix(c(1,0,0,1), nrow = 2, byrow = TRUE)
I
##      [,1] [,2]
## [1,]    1    0
## [2,]    0    1
charpoly(A, info = FALSE)
## [1]  1 -5 -2

Unfortunately i got stuck on assining a non numerical object to lambda and do the equation. My intention was to further use det() function to find the characteristic of the polynomial of the matrix.