If \(\begin{pmatrix} 6 & 4 \\ 7 & 5 \end{pmatrix}\) \(\begin{pmatrix} 2 \\ m \end{pmatrix}\) = 2\(\begin{pmatrix} 12 \\ 14.5 \end{pmatrix}\), find the value of m.
- 5
- 4
-
3
- 2
The correct answer is: C
Explanation
\(\begin{pmatrix} 6 & 4 \\ 7 & 5 \end{pmatrix}\) \(\begin{pmatrix} 2 \\ m \end{pmatrix}\) = 2\(\begin{pmatrix} 12 \\14.5 \end{pmatrix}\),
\(\begin{pmatrix} 6 \times 2 + 4 \times m \\ 7 \times 2 + 5 \times m \end{pmatrix}\) = \(\begin{pmatrix} 24 \\ 29 \end{pmatrix}\),
12 + 4m = 24
4m = 24 - 12 = 12, then, m = 3 or
14 + 5m = 29
5m = 29 - 14 = 15, then, m = 3