Eigen function and eigenvalues

Question

Questions:

Eigen function and eigenvalues

1. Consider a linear operator A^{^}with two sets of eigenfunctions and eigenvalues:

                                       A^{^}Ø_a = aØ_a,

                                       A^{^}Ø_b = bØ_b,

With a ≠ b. Now consider a linear combination of eigenfunction,  Φ = c1Øa + c2Øb. Show whether or not Φ is an eigenfunction of A^{^.}