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Exercise

Verifying the Math on Eigenvalues

In this exercise you'll find the eigenvalues \(\lambda\) of a matrix \(A\), and show that they satisfy the property that the matrix \(\lambda I - A\) is not invertible, with determinant equal to zero.

Instructions

100 XP
  • For the matrix A with the following R output:
     [,1] [,2]
[1,]    1    2
[2,]    1    1

find both eigenvalues.

  • Show that, for each eigenvalue lambda (\(\lambda\)), that the determinant of \(\lambda * I - A\) is equal to zero and hence the matrix \(\lambda * I - A\) is not invertible.