Finding a matrix representation of a Hamiltonian.

[helpmeprepls]

Homework Statement

The Hamiltonian H for a certain physical quantum mechanical system has three eigenvectors {|v1>, |v2>, |v3>} satisfying:
H|v_j> = (2-j)a|v_j>

Write down the matrix representing H in the representation {|v1>, |v2>, |v3>} .

Homework Equations

The Attempt at a Solution

I though the Hamiltonian would just be the eigenstates along the diagonal, however this seems too simple.
a 0 0
0 0 0
0 0 -a​

 

[blue_leaf77]

That's correct.