The benefit is reusing the matrix theory - matrix knowledge(!) - in different contexts. In some cases making a matrix in physics is a quite sterile representat

The benefit is reusing the matrix theory - matrix knowledge(!) - in different contexts. In some cases making a matrix in physics is a quite sterile representation, like you suggest, like plugging in the numbers in an otherwise generally stated question. The matrix values depend on choices of coordinate system and everything, quite inelegant in that way. Why practically use matrixes on the computer? It's efficient to compute in blocks instead of one by one.