Assume \(P, Q, R\) and \(W\) are matrices of order \(3 \times 3, a \times 4, b \times c\) and \(d \times a\) respectively. If \(PQ + WR\) is well defined, then the value of \(ab + cd\) is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 21
A product XY is defined only when the number of columns of X equals the number of rows of Y, and a sum needs both matrices of the same order.
PQ: P is \(3 \times 3\) and Q is \(a \times 4\), so
\(a = 3\), and PQ is of order \(3 \times 4\).
WR: W is \(d \times a = d \times 3\) and R is \(b \times c\), so
\(b = 3\), and WR is of order \(d \times c\).
For PQ + WR, the orders must match:
\(d \times c = 3 \times 4,\quad d = 3,\ c = 4\)
Hence
\(ab + cd = 3 \times 3 + 4 \times 3 = 9 + 12 = 21\)