For each eigenvalue, find the dimension of the corresponding eigenspace. (Enter your answers as a comma-separated list.)dim(xi)

To find the dimension of the eigenspace corresponding to each eigenvalue, we can follow these steps:

1. Start by finding the eigenvalues of the given matrix or linear transformation.
2. For each eigenvalue, solve the equation (A - λI)x = 0, where A is the matrix or linear transformation, λ is the eigenvalue, and I is the identity matrix.
3. Once you have the solutions for each eigenvalue, count the number of linearly independent vectors in each set of solutions.
4. The dimension of the eigenspace corresponding to each eigenvalue is equal to the number of linearly independent vectors in the set of solutions.

For example, if we have eigenvalues λ1, λ2, and λ3, and the corresponding eigenspaces have dimensions d1, d2, and d3 respectively, the answer would be: dim(xi) = d1, d2, d3.

Please note that the specific steps may vary depending on the context and the given matrix or linear transformation.