If \(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\)\(\begin{pmatrix} 5 \\ 4 \end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\), find the value of k.
- 1.2
- 3.6
-
0.8
- 0.5
The correct answer is: C
Explanation
\(\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix}\)\(\begin{pmatrix} 5 \\ 4 \end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\)
\(\begin{pmatrix} 10 + 4 \\ 20 + 12\end{pmatrix}\) = \(\begin{pmatrix} 14 \\ 32\end{pmatrix}\) = k\(\begin{pmatrix} 17.5 \\ 40.0 \end{pmatrix}\)
k = \(\frac{14}{17.5} = \frac{32}{40} = 0.8\)