Computing Eigenvectors in R

In this exercise you'll find the eigenvectors of a matrix, and show that they satisfy the properties discussed in the lecture.

For the matrix A with the following R output:

  [,1] [,2]
[1,]    1    2
[2,]    1    1

find eigenvectors corresponding to the two eigenvalues (recall that there are infinitely many of each, but R will only report one for each).

Print both eigenvectors.
Show that, for each eigenvalue/eigenvector pair, \(A\vec{v} = \lambda \vec{v}\).