Identify if a column in a matrix is the product of other columns of the same matrix

Question

I read that linear transformation can be used to identify the linear combination between the columns(or rows) of a matrix.

Is there any way to identify the product between the columns?

Eg : Given this matrix, is there any way to identify that C3 = C2 * C1

$$ \begin{pmatrix} 1 & 5 & 5 \\ 2 & 7 & 14 \\ 3 & 11 & 33 \\ \end{pmatrix} $$