Chapter 10.2, Problem 7P

Following what we did in equations (2.14) to (2.17), show that the direct product of a vector and a 3^rd-rank tensor is a 4^th-rank tensor. Also show that the direct product of two 2^nd-rank tensors is a 4^th-rank tensor. Generalize this to show that the direct product of two tensors of ranks $m$ and $n$ is a tensor of rank $m+n$.