EXM.2.AHL.TZ0.5

pestleMathematicsAIHLPaper 2EXM· ahl-1-14-introduction-to-matricessource ↗

Let A = $\left( {\begin{array}{*{20}{c}} a&b \\ c&0 \end{array}} \right)$ and B = $\left( {\begin{array}{*{20}{c}} 1&0 \\ d&e \end{array}} \right)$ . Giving your answers in terms of $a$ , $b$ , $c$ , $d$ and $e$ ,

write down A + B.

[2]

find AB.

[4]

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

A + B = $\left( {\begin{array}{*{20}{c}} a&b \\ c&0 \end{array}} \right) + \left( {\begin{array}{*{20}{c}} 1&0 \\ d&e \end{array}} \right)$

$= \left( {\begin{array}{*{20}{c}} {a + 1}&b \\ {c + d}&e \end{array}} \right)$ A2

[2 marks]

AB = $\left( {\begin{array}{*{20}{c}} a&b \\ c&0 \end{array}} \right) + \left( {\begin{array}{*{20}{c}} 1&0 \\ d&e \end{array}} \right)$ A1A1A1A1

Note: Award N2 for finding BA = $\left( {\begin{array}{*{20}{c}} a&b \\ {ad + ce}&{bd} \end{array}} \right)$ .

[4 marks]

Examiners’ report

[N/A]