Question

1 2 1 -1 0 1

Answer 1

the matrix can be diagonalized if there exists an invertible matrix P and diagonal matrix D

such that A = PDP^-1

1 2 1 1 0 0 det!|-101|-시010 1 1 00 0 1 The eigenvalues are: -1,0

eigenvalues are 1, 0

eigenvectors are

$\begin{bmatrix} 3/2\\ -1/2\\ 1 \end{bmatrix}$, $\begin{bmatrix} 1\\ -1\\ 1 \end{bmatrix}$

since there are 2 eigenvectors which is less thyan 3 , so the matrix cannot be diagonalized