What Is the Dimension of Eigenspaces for Given Characteristic Polynomial?

[Mark53]

Homework Statement

For c not equal to ±1, what is the dimension of the eigenspaces of A

The characteristic polynomial of A is (x-1)(x+1)(x-c)

The Attempt at a Solution

each term in the characteristic polynomial has a multiplicity of 1 so does this mean that the dimension of the eigenspaces is also 1?

 

[Mark44]

Thread moved. Questions about eigenspaces and the like are well beyond the precalculus level.

Homework Statement

For c not equal to ±1, what is the dimension of the eigenspaces of A

The characteristic polynomial of A is (x-1)(x+1)(x-c)

The Attempt at a Solution

each term in the characteristic polynomial has a multiplicity of 1 so does this mean that the dimension of the eigenspaces is also 1?

Yes, I believe so. Do you know why they specified that c ≠ 1 and c ≠ -1?

 

[Mark53]

Thread moved. Questions about eigenspaces and the like are well beyond the precalculus level.
Yes, I believe so. Do you know why they specified that c ≠ 1 and c ≠ -1?

because it would change the multiplicity of the polynomial