For each of the following, answer whether it makes sense to multiply the matrices of the given sizes. In each case where it makes sense, demonstrate an example in Excel, where you can make up the numbers.

a. AB, where A is 3 4 and B is 4 1

b. AB, where A is 1 4 and B is 4 1

c. AB, where A is 4 1 and B is 1 4

d. AB, where A is 1 4 and B is 1 4

e. ABC, where A is 1 4, B is 4 4, and C is 4 1

f. ABC, where A is 3 3, B is 3 3, and C is 3 1 g. ATB, where A is 4 3 and B is 4 3, and AT denotes the transpose of A