EXM.1.AHL.TZ0.25

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

Consider the matrix A = $\left( {\begin{array}{*{20}{c}} 0&2 \\ a&{ - 1} \end{array}} \right)$ .

Find the matrix A².

[2]

If det A² = 16, determine the possible values of $a$ .

[3]

Markscheme / solution

A² = $\left( {\begin{array}{*{20}{c}} {2a}&{ - 2} \\ { - a}&{2a + 1} \end{array}} \right)$ (M1)A1

[2 marks]

METHOD 1

det A² = $4{a^2} + 2a - 2a = 4{a^2}$ M1

$a$ = ±2 A1A1 N2

METHOD 2

det A = $- 2a$ M1

det A = ±4

$a$ = ±2 A1A1 N2

[3 marks]

Examiners’ report

[N/A]