Ertercise 6.2. Even and odd eigenfunctions. (a) Prove that if n is a function on [1, 1] that is neither even nor odd, then um\") and u(a:) are linearly independent. (5) Let L be an \"even\" linear operator on [1,1] in the sense that if L maps u(;z:) to v(a:), then it maps u(:z:) to \"(K:13). Prove that if 'U(E) is an eigenfunction of L with eigenvalue A, then 'U(E) is an eigenfunction of L with the same A. (c) Assuming the eigenvalues of L are all of multiplicity one, ShOW that every eigenfunction of L is either even or odd