DAT 605 - Wk 3 Discussion Reply

Beezer: A First Course in Linear Algebra, Pg 389

• Exerices C27 in R

library(matlib)
library(MASS)

A <- matrix(c(0,4,-1,1,-2,6,-1,1,-2,8,-1,-1,-2,8,-3,1), nrow=4, byrow=T)

A

##      [,1] [,2] [,3] [,4]
## [1,]    0    4   -1    1
## [2,]   -2    6   -1    1
## [3,]   -2    8   -1   -1
## [4,]   -2    8   -3    1

eigen(A)

## eigen() decomposition
## $values
## [1]  4 -2  2  2
## 
## $vectors
##      [,1]          [,2]       [,3]       [,4]
## [1,] -0.5  1.133117e-16 -0.5724117 -0.7559289
## [2,] -0.5  9.064933e-17 -0.4199867 -0.3779645
## [3,] -0.5 -7.071068e-01 -0.6875483 -0.3779645
## [4,] -0.5 -7.071068e-01 -0.1524250 -0.3779645