Assume A, B and C are matrices of order \(m \times n, n \times 3\) and \(3 \times q\) respectively. The restrictions on \(m,n\) and \(q\) so that \(AB + BC\) is defined are
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(m = n,q=3\)
A product PQ is defined when the number of columns of P equals the number of rows of Q:
\((m \times n)(n \times 3)\): AB is defined and has order \(m \times 3\)
\((n \times 3)(3 \times q)\): BC is defined and has order \(n \times q\)
A sum of matrices is defined only when both have the same order:
\(m \times 3 = n \times q\)
\(m = n,\quad q = 3\)