Problem C11

knitr::include_graphics('3.png')

# Loading the library

library(pracma)
library(dplyr)
## 
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
## 
##     filter, lag
## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union
# Create matrix to feed data into R

A <- matrix(c(3,0,1,2,1,2,1,1,0), nrow=3)
A
##      [,1] [,2] [,3]
## [1,]    3    2    1
## [2,]    0    1    1
## [3,]    1    2    0
# Now let's find out the characteristic polynomial of the defined matrix

A %>% charpoly()
## [1]  1 -4  0  5

Conclusion

The characteristic polynomial of above matrix is 1, -4, 0 and 5.