Consider the left shift operator on the space of infinite sequences of complex numbers:

Question

L(z1,z2,…)=(z2,z3,…).
Is L injective?

Yes <text> Yes</text> - incorrect No
Is L surjective?

Yes <text> Yes</text> - correct No
Find the eigenvalues and eigenvectors of L. Then complete the following sentence.

The complete set of eigenvalues of L is

0 <text> 0</text> - incorrect 1 0 and 1 all integers all real numbers all complex numbers
Let λ be an eigenvalue, the associated eigenvectors are :

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