When I was in high school my math teacher taught such "diagonal rule" of calculating 3D determinants as well. She did not explain the reason behind it but it is a very convenient way to calculate the value(also in dot product)
dranzer
I think it is very useful to have determinants represented in the recursive notation of the sub matrices for programming.
jacheng
IF the determinant is 0, it can tell you that your vectors are not lineraly independent
bcagan
It is definitely interesting to see how equations that may behave in a general manner sometimes start to have unique edge cases as you get to the smallest cases. For instance, the diagonal rule would be impossible or at least be far far less convenient than proper calculation if you tried to do it on a 4x4 or larger matrix, but the way the determinant behaves in 2x2 and 3x3 matrices just so happens to allow for the diagonal rule to work. When I took linear algebra in high school, our teacher had us write out all the combinations by hand just to show us why we use this method instead.
When I was in high school my math teacher taught such "diagonal rule" of calculating 3D determinants as well. She did not explain the reason behind it but it is a very convenient way to calculate the value(also in dot product)
I think it is very useful to have determinants represented in the recursive notation of the sub matrices for programming.
IF the determinant is 0, it can tell you that your vectors are not lineraly independent
It is definitely interesting to see how equations that may behave in a general manner sometimes start to have unique edge cases as you get to the smallest cases. For instance, the diagonal rule would be impossible or at least be far far less convenient than proper calculation if you tried to do it on a 4x4 or larger matrix, but the way the determinant behaves in 2x2 and 3x3 matrices just so happens to allow for the diagonal rule to work. When I took linear algebra in high school, our teacher had us write out all the combinations by hand just to show us why we use this method instead.