The matrix A=(100021002)A = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 2 & 1 \\ 0 & 0 & 2 \end{pmatrix}A=100020012 is NOT diagonalizable. Which is the correct reason?
The determinant is zero.
It is an upper triangular matrix.
The eigenvalue λ=2\lambda = 2λ=2 has geometric multiplicity 1, but algebraic multiplicity 2.
It is missing a zero eigenvalue.