I have the matrix
\begin{bmatrix} 4 & 1 & -1 \\ 2 & 5 & -2 \\ 1 & 1 & 2 \end{bmatrix}
And the eigenvalues 5, 3, 3.
The eigenspace with eigenvalue 3 has dimension 2 (rank 1). No doubt.
However, for eigenvalue 5, $A-5I$ has rank 2. Till that point I agree with my professor’s solution. But shouldn’t the dimension of the eigenspace be $3-2 = 1$? According to my textbook, the dimension is 2.