The execution of the MATLAB command help gallery contains the following entry “gallery(5) is an interesting eigenvalue problem. Try to find its  eigenvalues and eigenvectors.” Let and request double...

The execution of the MATLAB command help gallery contains the following entry

“gallery(5) is an interesting eigenvalue problem. Try to find its
 eigenvalues and eigenvectors.”

Let

and request double precision output using format long.

 Execute eig(A), and compute

<sub>i

i

i
2</sub>

 Compute det and rank Why does the output of both commands conflict with the results of

 Approximate the characteristic polynomial of
 using p = poly What do you believe is the actual characteristic polynomial,

 The Cayley-Hamilton theorem states that every matrix satisfies its characteristic equation. Compute
 where
 is the assumed characteristic polynomial from part
 Is the result close to zero

 Explain why this matrix causes so much trouble for eigenvalue solvers.