Final answer:
When the last column of the product AB is all zeros and B has no column of zeros, it can be concluded that the columns of matrix A are linearly dependent.
Step-by-step explanation:
When the last column of the product AB is entirely zeros but B itself has no column of zeros, we can conclude that the columns of matrix A are linearly dependent. This means that at least one column of A can be expressed as a linear combination of the other columns.
This can be understood by considering the product AB. The columns of AB are formed by multiplying each column of A with each corresponding column of B and then summing them. If the last column of AB is all zeros, it means that the linear combination of the columns of A that corresponds to the last column of AB is equal to zero. This implies that the columns of A must be linearly dependent.