WAEC 2022 · Paper 1 · Q11

Matrices & linear transformations

If $\begin{pmatrix} 2 & -3 \\ 1 & 4 \end{pmatrix}\begin{pmatrix} -6 \\ k \end{pmatrix} = \begin{pmatrix} 3 \\ -26 \end{pmatrix}$ , find the value of $k$ .

Worked solution (try it first)

Multiply the first row by the column: $2(-6) + (-3)k = 3$ , so $-12 - 3k = 3$ .
Add 12 to both sides: $-3k = 15$ , so $k = -5$ .
Check with the second row: $1(-6) + 4(-5) = -26$ .
So $k = -5$ , option B.

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