If \(\begin{bmatrix} 1 & 2\\ 3 & 4\end{bmatrix}\begin{bmatrix} 3 & 1\\ 2 & 5\end{bmatrix} = \begin{bmatrix} 7 & 11\\ \mathrm{K} & 23\end{bmatrix}\), then value of K is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 17
K is the entry in row 2, column 1 of the product. By row-by-column multiplication, it is row 2 of the first matrix times column 1 of the second:
\(\mathrm{K} = 3 \times 3 + 4 \times 2\)
\(= 9 + 8 = 17\)
(The other entries check: 1 × 3 + 2 × 2 = 7, 1 × 1 + 2 × 5 = 11, 3 × 1 + 4 × 5 = 23.)