DATA_605_Discussion_Response_3__C12_p388_Thonn

** DATA_605_Discussion_3__C12_p388_Thonn **

** Problem C10 pg388 **

1-1). Find characterisic polynomial

\(A = \left[\begin{array}{rrrr} 1 & 2 & 1 & 0 \\ 1 & 0 & 1 & 0 \\ 2 & 1 & 1 & 0 \\ 3 & 1 & 0 & 1 \end{array} \right]\)

\(det (A - \lambda I) = 0\)

** Problem C10 pg 388 in R **

Note: the syntax for polyroot is polyroot(c(C, B, A)) gives the roots of Ax^2 + Bx + C.

#install.packages("pracma")

library(pracma)

## Warning: package 'pracma' was built under R version 3.3.3

A <- matrix (c (1,2,1,0, 1,0,1,0,  2,1,1,0,  3,1,0,1), nrow = 4, ncol=4 , byrow = TRUE)
A

##      [,1] [,2] [,3] [,4]
## [1,]    1    2    1    0
## [2,]    1    0    1    0
## [3,]    2    1    1    0
## [4,]    3    1    0    1

#characteristic polynomial - R
charpoly(A, info=FALSE)

## [1]  1 -3 -2  2  2

# [1]  1 -3 -2 2 2

characteristic polynomial

\(1\lambda^4 -3\lambda^3 -2\lambda^2 + 2\lambda^2 + 2 = 0\)

# Roots - R
a = round(polyroot(c ( 1, -3, -2, 2, 2)),2)
a

## [1]  0.30+0.0i -1.15+0.6i -1.15-0.6i  1.00+0.0i

# roots of characteristic equation
#[1]  0.30+0.0i -1.15+0.6i -1.15-0.6i  1.00+0.0i

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