Suppose that A, B and C are matrices of order \(m \times n,\ n \times 5\) and \(5 \times q\) respectively. The restriction on \(m, n\) and \(q\) so that AB-BC is defined are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(m = n,\ q = 5\)
A difference AB − BC is defined only when AB and BC both exist and have the same order.
A is \(m \times n\) and B is \(n \times 5\), so AB exists and
AB is of order \(m \times 5\)
B is \(n \times 5\) and C is \(5 \times q\), so BC exists and
BC is of order \(n \times q\)
Equating the orders \(m \times 5\) and \(n \times q\):
\(m = n,\quad q = 5\)