please help me solving this question uding linear algebra

u a I.) 1 u}: A \\ ; 4. (5 points) Let 5 2 6 1 0 3 8 0 A: 0 0 5 1 0 0 0 1 Find the characteristic equation and the eigenvalues for A. List the algebraic multiplic- ity of each eigenvalue and for any eigenvalue with algebraic multiplicity strictly greater than 1, nd the corresponding eigenspace (Hint: Notice that the matrix is upper tri- angular, so the eigenvalues are easy to nd. The eigenvalues and their multiplicities should be listed in a table. You are only asked to nd one eigenspace, please do not include more than this.)