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.

Question

Mathematics

Ingrid Gibson

13 November, 05:16

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.

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Answers (1)

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Natalee Walton · Answer 1

True

Step-by-step 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.

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.

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.