If \(\begin{bmatrix}1&3\\2&4\end{bmatrix}\begin{bmatrix}3&5\\-1&3\end{bmatrix} = \begin{bmatrix}m&14\\2&n\end{bmatrix}\), then \(m+n\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 22
By matrix multiplication (row of the first × column of the second), only the entries in the positions of m and n are needed:
\(m = 1(3) + 3(-1) = 3 - 3 = 0\)
\(n = 2(5) + 4(3) = 10 + 12 = 22\)
\(m + n = 0 + 22 = 22\)
The other two entries, \(1(5) + 3(3) = 14\) and \(2(3) + 4(-1) = 2\), agree with the given matrix.