If P = \(\begin {pmatrix} 2 & 3\\ -4 & 1 \end {pmatrix}\), Q =
FURTHER MATHEMATICS
WAEC 2019
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: C. \(\frac{4}{5}\)
Explanation
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 = \(\frac{36}{45}\)
= \(\frac{4}{5}\)
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