The geometric multiplicity is the dimension of the eigenspace corresponding to your eigenvalue. That is, when you solve
how many arbitrary parameters do you get? That'll be the geometric multiplicity.
let A be the matrix
|4 1 0 0 0|
|0 4 1 0 0|
|0 0 4 1 0|
|0 0 0 4 1|
|0 0 0 0 4|
I am asked to find the algebraic multiplicity
and the geometric multiplicity
I think as it is an upper triangular matrix eigenvalues are the diagonal entries i.e. all 4,
4^5 so Am is 5, im not sure on the geometric multiplicity though. Any help appreciated!