EXM.1.AHL.TZ0.32

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

If A = $\left( {\begin{array}{*{20}{c}} 1&2 \\ k&{ - 1} \end{array}} \right)$ and A² is a matrix whose entries are all 0, find $k$ .

Markscheme / solution

A² = $\left( {\begin{array}{*{20}{c}} 1&2 \\ k&{ - 1} \end{array}} \right)\left( {\begin{array}{*{20}{c}} 1&2 \\ k&{ - 1} \end{array}} \right)$ M1

$= \left( {\begin{array}{*{20}{c}} {1 + 2k}&0 \\ 0&{2k + 1} \end{array}} \right)$ A2

Note: Award A2 for 4 correct, A1 for 2 or 3 correct.

$1 + 2k = 0$ M1

$k = - \frac{1}{2}$ A1

[5 marks]

Examiners’ report

[N/A]