If P = \(\begin {pmatrix} 2 & 3\\  -4 & 1 \end {pmatrix}\), Q = \(\begin{pmatrix} 6 \\ 8 \end {pmatrix}\) and PQ = k \(\begin {pmatrix} 45\\ -20 \end {pmatrix}\). Find the value of k.

A.

-\(\frac{5}{4}\)

B.

-\(\frac{4}{5}\)

C.

\(\frac{4}{5}\)

D.

\(\frac{5}{4}\)

Correct answer is C

PQ = \(\begin {pmatrix} 2 & 3\\ -4 & 1\end {pmatrix}\) = \(\begin {pmatrix} 6 \\ 8 \end {pmatrix}\) = \(\begin {pmatrix} 36 \\ - 16\end {pmatrix}\)

\(\begin {pmatrix} 36 \\ -16 \end {pmatrix} \) = k = \(\begin {pmatrix} 45 \\ -20 \end {pmatrix} \)

k = \(\frac{36}{45}\) 

= \(\frac{4}{5}\)