Question

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disaproves the statement.

If Ax=ax for a square matrix A, vector x, and scalar a, where x=/0, then a is an eigenvalue of A.

Answer 1

True

Explanation:

This statement is true, basically by the definition of eigenvalue. An eigenvalue is a scalar λ such that there exist a nonzero vector v which satisfies Av = λv. Naturally, the given value a satisfies this hypothesis, hence it is an eigenvalue, as we wanted to show.