K. Nicole Clark k-clark

4/30/2004

URL: people.tamu.edu/~knc8928/8.1.24.pdf

8.1.24 – Find the eigenvalues and eigenvectors of the given matrix. Remark upon any case where an eigenbasis of real eigenvectors does not exist.

Solution

Using the rule , where A is the matrix given above, it is easy to find our eigenvalues.

Thus, there is only one eigenvalue for this matrix, .

Now we will find the eigenvectors associated with the above eigenvalue, using the rule

.

Thus, the corresponding eigenvectors are of the form .

You could also say that the eigenvectors .