Chapter 7.1, Problem 48E

Eigenvalues and Eigenvectors of Linear Transformations In Exercises 45-48, consider the linear transformation $T$: $R^n\to R^n$ whose matrix $A$ relative to the standard basis is given. Find (a) the eigenvalues of $A$, (b) a basis for each of the corresponding eigenspaces, and (c) the matrix $A\text{'}$ fot $T$ relative to the basis $B\text{'}$, where $B\text{'}$ is made up of the basis vectors found in part (b).

$\left[\begin{array}{ccc}3& 1& 4\\ 2& 4& 0\\ 5& 5& 6\end{array}\right]$