Question

Consider the matrices of the possible matrix products, which make sense?

1) (acb, bac, cab) only
2) (acb, bac, cba) only
3) (abc, bca, cab) only
4) All of them
5) None of them

Answer 1

The second matrix product (acb, bac, cba) only makes sense. So the correct answer is option 2.

Step-by-step explanation:

In order for matrix multiplication to make sense, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Let's analyze the given options:

1. (acb, bac, cab) -> The second matrix has 3 columns, while the third matrix has 2 rows, so this product does not make sense.
2. (acb, bac, cba) -> The second matrix has 3 columns and the third matrix has 3 rows, so this product makes sense.
3. (abc, bca, cab) -> The first matrix has 3 rows and the second matrix has 3 columns, so this product makes sense.
4. All of them -> This is not correct because the first option does not make sense.
5. None of them -> This is not correct because the second and third options make sense.

Therefore, the correct answer is option 2) (acb, bac, cba) only.