Given: A=−2−1−4 and B=[−123]
The prime symbol (') denotes the transpose operation. For a column vector, the transpose produces a row vector, and for a row vector, the transpose produces a column vector.
A=−2−1−4 is a column vector with 3 rows and 1 column.
A′=[−2−1−4] is a row vector with 1 row and 3 columns.
B=[−123] is a row vector with 1 row and 3 columns.
B′=−123 is a column vector with 3 rows and 1 column.
A′B′=[−2−1−4]×−123
A′B′=(−2)(−1)+(−1)(2)+(−4)(3)
A′B′=2−2−12
A′B′=−12
Therefore, the value of A′B′ is −12.