Discussion 3

C19† Find the eigenvalues, eigenspaces, algebraic multiplicities and geometric multiplicities for the matrix below. It is possible to do all these computations by hand, and it would be instructive to do so.

#Defining the matrix C
C <- matrix(c(-1, 2, -6, 6), nrow = 2, byrow = TRUE)

#Finding eigenvalues and eigenvectors
eigen_result <- eigen(C)

#Extracting eigenvalues and eigenvectors
eigenvalues <- eigen_result$values
eigenvectors <- eigen_result$vectors

#Displaying the results
cat("Eigenvalues:\n")

## Eigenvalues:

print(eigenvalues)

## [1] 3 2

cat("\nEigenvectors:\n")

## 
## Eigenvectors:

print(eigenvectors)

##            [,1]       [,2]
## [1,] -0.4472136 -0.5547002
## [2,] -0.8944272 -0.8320503

```