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WAEC Further Mathematics 2022 Paper

Question : 16

Total: 45

Given:

\begin{vmatrix} 2 & -3 \\ 1 & 4 \end{vmatrix}\begin{vmatrix} -6 \\ k \end{vmatrix}\begin{vmatrix} 3 \\ -26 \end{vmatrix}=15

k

Solution:

Concept:

Use matrix multiplication and equate the corresponding entries of the resulting column matrix.

Explanation:

Multiply the

2 \times 2

matrix by the column matrix

\begin{pmatrix}-6 \\ k\end{pmatrix}

\begin{pmatrix}2 & -3 \\ 1 & 4\end{pmatrix}\begin{pmatrix}-6 \\ k\end{pmatrix} = \begin{pmatrix}2(-6)+(-3)k \\ 1(-6)+4k\end{pmatrix} = \begin{pmatrix}-12-3k \\ -6+4k\end{pmatrix}.

Equate this result to

\begin{pmatrix}3 \\ -26\end{pmatrix}

Equating the first entries gives

-12-3k=3

-3k=15

, which gives

k=-5

Check using the second entry:

-6+4(-5)=-26

, so it is consistent.

Answer:

k=-5

Option B.

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