Chapter E

C24 Find the eigenvalues,eigenspaces,algebraic and geometric multiplicities for A =

Given the matrix $A = \[\begin{pmatrix} 1 & -1 & 1 \\ -1 & 1 & -1 \\ 1 & -1 & 1 \end{pmatrix}\]

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

print(A)

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

EigenValues

eigenvalues <- round(eigen(A)$values,1)


print(eigenvalues)

## [1] 3 0 0

eigenvectors <- round(eigen(A)$vectors)

print(eigenvectors)

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