Since the fourth column of B has been linearly represented by the first three columns, the rank of B is at most 3.

This condition also shows that the first three columns of B are linearly related, so the rank of B is at most 2.

If the topic is correct and there are no other conditions, the rank of B can be 0, 1, 2.

(1) Because we take a 1=a2=a3=' (a prime number means transpose), then B is a simple zero matrix, so the rank is 1.

(2) If A 1 = A2 = A3 =', then the rank of B is 2.