Question 24: Certain 2D kernel K can be decomposed into two 1D kernel…

Certain 2D kernel $K$ can be decomposed into two 1D kernels ($v$ and $h$) to reduce the computation cost such as $K = vh^\top$. The 2D kernel is called as Separable Kernel.

Consider the following 2D kernels

$\text{(a)} \quad \begin{bmatrix} 2 & 4 & 6 \\ 3 & 6 & 9 \\ 1 & 2 & 3 \end{bmatrix}$

$\text{(b)} \quad \begin{bmatrix} 2 & 4 & 6 \\ 3 & 6 & 9 \\ 2 & 3 & 4 \end{bmatrix}$

$\text{(c)} \quad \begin{bmatrix} 5 & 0 & 5 \\ 10 & 0 & 10 \\ -5 & 0 & 5 \end{bmatrix}$

$\text{(d)} \quad \begin{bmatrix} 5 & 0 & 5 \\ 10 & 0 & 10 \\ -5 & 0 & -5 \end{bmatrix}$

Which of the above kernels are separable?