K. Nicole Clark k-clark

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 _{}.