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 y is an eigenvector of A, then Ay=ky for some scalar k.

Answer 1

See explanation below.

Explanation:

True by definition of eigenvector. If y is an eigenvector of the matrix A, then we need to satisfy this condition:

`Ay= ky`

For some eigenvalue k.

The definition is the following:

"Any non zero vector x that satisfies
`Ax = \lambda x` for some value
`\lambda` is called an eigenvector of the linear operator A, and
`\lambda` is called the corresponding eigenvalue"