EXM.1.AHL.TZ0.47

pestleMathematicsAIHLPaper 1EXM· ahl-1-15-eigenvalues-and-eigenvectorssource ↗

Given that A = $\left( {\begin{array}{*{20}{c}} 3&{ - 2} \\ { - 3}&4 \end{array}} \right)$ and I = $\left( {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right)$ , find the values of $\lambda$ for which (A – $\lambda$ I) is a singular matrix.

Markscheme / solution

singular matrix ⇒ det = 0 (R1)

$\left| {\begin{array}{*{20}{c}} {3 - \lambda }&{ - 2} \\ { - 3}&{4 - \lambda } \end{array}} \right|$ (A1)

$\left( {3 - \lambda } \right)\left( {4 - \lambda } \right) - 6 = 0$ (M1)

$\Rightarrow {\lambda ^2} - 7\lambda + 6 = 0$ (A1)

$\lambda = 1$ or 6 (A1)(A1) (C6)

Note: Award (C2) for one correct answer with no working.

[6 marks]

Examiners’ report

[N/A]