DATA_605_Discussion_3__C10_p388_Thonn

** DATA_605_Discussion_3__C10_p388_Thonn **

** Problem C10 pg388 - manual method **

1-1). Find characterisic polynomial

\(A = \left[\begin{array}{rrrr} 1 & 2 \\ 3 & 4 \\ \end{array} \right]\)

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

$[ \[\begin{array}{rrrr} 1 & 2 \\ 3 & 4 \\ \end{array}\] ] - [ \[\begin{array}{rrrr} -\lambda +1 & 2 \\ 3 & -\lambda +1 \\ \end{array}\]

] $

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

characteristic polynomial - manual

\(\lambda^2 -5\lambda - 2 = 0\)

** 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

# Roots - R
a = round(polyroot(c(-2,-5,1)),2)
a

## [1] -0.37+0i  5.37+0i

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

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

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

## [1]  1 -5 -2

# [1]  1 -5 -2

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