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WAEC Further Mathematics 2011 Paper

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Question : 18

Total: 40

If

\begin{pmatrix} 3 & 2 \\ 7 & x \end{pmatrix} \binom{2}{3} = \binom{12}{29}

x

.

5
6
7
8

Solution:

Concept:

Matrix multiplication followed by equating corresponding entries to solve for

x

.

Explanation:

Multiply the

2 \times 2

matrix by the column vector.

\begin{pmatrix} 3 & 2 \\ 7 & x \end{pmatrix} \binom{2}{3} = \binom{3 \times 2 + 2 \times 3}{7 \times 2 + x \times 3}

This equals

\binom{12}{29}

.

The top entry gives

6 + 6 = 12

, which is correct.

The bottom entry gives

14 + 3x = 29

.

So

3x = 29 - 14 = 15

.

Thus

x = \frac{15}{3} = 5

.

Answer:

x = 5

, which is option A.

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