If `v` is an eigenvector of `A` with corresponding eigenvalue `lambda` and `c` is a scalar, show that `v` is an eigenvector of `A-cI` with corresponding eigenvalue `lambda-c.` I'm not sure where to...

If `v` is an eigenvector of `A` with corresponding eigenvalue `lambda` and `c` is a scalar, show that `v` is an eigenvector of `A-cI` with corresponding eigenvalue `lambda-c.`

I'm not sure where to start here. 

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Just start from what you're given and the definitions. Since `v` is an eigenvector of `A` with eigenvalue `lambda` , we have

`Av=lambda v.`

For `v` to...

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