The MATLAB command where alpha is a scalar, returns the symmetric matrix alpha eye(n) + ones(n). The default for alpha is  and the matrix is singular for alpha equal to 0. The eigenvalues are      For...

The MATLAB command

where alpha is a scalar, returns the symmetric matrix alpha eye(n) + ones(n). The default for alpha is
 and the matrix is singular for alpha equal to 0. The eigenvalues are

     For parts
 and
 use
 eigsymj,
 eigsymqr,
 eigsymb, and
 dconquer, to compute the eigenvalues. In each case, compute

<sub>i

2</sub>, where
 are the exact eigenvalues. Do these methods handle the eigenvalues of multiplicity
 properly

 alpha

alpha

 Let A = gallery(’pei’,5,3), and compute the eigenvector matrix V1 and the corresponding diagonal matrix D1 of eigenvalues. Perturb A(5,1) by

⁻⁸
and find matrices V2 and D2. Compute

₂
 and list the eigenvectors V1 and V2. Explain the results.