If you have a matrix, a 2x2 say
and supposing it is in some way expanded into a 3x3 matrix so that the third row or column is formed from some kind of multiplication of the first two, such as
I was wondering if this process has a name because I am having trouble finding anything about it online. The reason for including a new row is because I am studying determinants and wanted to keep the matrix square. The determinant won't be zero because we multiplied two rows together rather than adding them.
Does this have a name and, if it is common enough to have a name, what does this process mean geometrically? There is a rule for adding rows or columns but not for multiplying.
Thanks. If I've not been clear I can try to be more so.