Determine in each of the following cases if the function in the first column is

Question

Determine in each of the following cases if the function in the first column is an eigenfunction of the operator in the second column. If so, what is the eigenvalue?

Explanation / Answer

Given a vector space V, over a field F, and a linear function A:V -> V (that is for x,y in V and 'a' in F then A(ax+y)=aA(x)+A(y) ), e in F is an eigenvalue of A if there is a non-zero vector v in V such that A(v)=ev. The more specific meaning used in a linear algebra class is, if you have a NxN matrix A then e (where e is a rational/real/complex number) is an eigenvalue for A if there is an N dimensional vector v such that Av=ev.

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