I wonder whether there is a simple way(e.g. if asked in exam) to determine if a matrix is separable. If yes, how can we write the separated parts? For example, Gaussian Blur kernel is separable.
$$\frac1{256}\cdot\begin{bmatrix} 1&4&6&4&1\\ 4&16&24&16&4\\ 6&24&36&24&6\\ 4&16&24&16&4\\ 1&4&6&4&1 \end{bmatrix} = \frac1{256}\cdot\begin{bmatrix} 1\\4\\6\\4\\1 \end{bmatrix}\cdot\begin{bmatrix} 1&4&6&4&1 \end{bmatrix} $$
I have two matrices asked in old-exams. How to do my wish on the following matrices?
$$A = \frac1{4}\cdot\begin{bmatrix} -1&-2&-1\\ -2&16&-2\\ -1&-2&-1\\ \end{bmatrix} $$
$$B = \begin{bmatrix} -1&-3&-1\\ 0&0&0\\ 1&3&1\\ \end{bmatrix} $$