EXM.1.AHL.TZ0.44

pestleMathematicsAIHLPaper 1EXM· ahl-1-14-introduction-to-matricessource ↗

Find the values of the real number $k$ for which the determinant of the matrix $\left( {\begin{array}{*{20}{c}} {k - 4}&3 \\ { - 2}&{k + 1} \end{array}} \right)$ is equal to zero.

Markscheme / solution

$\left| {\begin{array}{*{20}{c}} {k - 4}&3 \\ { - 2}&{k + 1} \end{array}} \right| = 0$

$\Rightarrow \left( {k - 4} \right)\left( {k + 1} \right) + 6 = 0$ (M1)

$\Rightarrow {k^2} - 3k + 2 = 0$ (M1)

$\Rightarrow \left( {k - 2} \right)\left( {k - 1} \right) = 0$

$\Rightarrow k = 2$ or $k = 1$ (A1) (C3)

[3 marks]

Examiners’ report

[N/A]