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WAEC Further Mathematics 2017 Paper

Question : 12

Total: 40

\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix} \binom{5}{4} = k \binom{17.5}{40.0}

k

Solution:

Concept:

Matrix multiplication followed by comparing corresponding entries to solve for

k

Explanation:

First, multiply the matrix by the column vector.

\begin{pmatrix} 2 & 1 \\ 4 & 3 \end{pmatrix} \binom{5}{4} = \binom{2(5)+1(4)}{4(5)+3(4)}

This simplifies to:

\binom{10+4}{20+12} = \binom{14}{32}

The given equation is:

\binom{14}{32} = k \binom{17.5}{40.0}

Compare the first components:

14 = k(17.5)

k = \frac{14}{17.5} = 0.8

Check with the second components:

32 = k(40.0) \Rightarrow k = \frac{32}{40} = 0.8

Both comparisons give the same value of

k

Answer:

k = 0.8

Correct option: C. 0.8

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