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.

A.

1.2

B.

3.6

C.

0.8

D.

0.5

Correct answer is C

\(\begin{pmatrix}  2  &  1 \\  4 & 3 \end{pmatrix}\)\(\begin{pmatrix}  5 \\ 4 \end{pmatrix}\)  = 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 = \(\frac{14}{17.5} = \frac{32}{40} = 0.8\)