EXM.1.AHL.TZ0.11

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

Let A = $\left( {\begin{array}{*{20}{c}} 1&2 \\ 3&{ - 1} \end{array}} \right)$ and B = $\left( {\begin{array}{*{20}{c}} 3&0 \\ { - 2}&1 \end{array}} \right)$ .

Find A + B.

[2]

Find −3A.

[2]

Find AB.

[3]

Markscheme / solution

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

evidence of addition (M1)

eg at least two correct elements

A + B = $\left( {\begin{array}{*{20}{c}} 4&2 \\ 1&0 \end{array}} \right)$ A1 N2

[2 marks]

evidence of multiplication (M1)

eg at least two correct elements

−3A = $\left( {\begin{array}{*{20}{c}} { - 3}&{ - 6} \\ { - 9}&3 \end{array}} \right)$ A1 N2

[2 marks]

evidence of matrix multiplication (in correct order) (M1)

eg AB = $\left( {\begin{array}{*{20}{c}} {1\left( 3 \right) + 2\left( { - 2} \right)}&{1\left( 0 \right) + 2\left( 1 \right)} \\ {3\left( 3 \right) + \left( { - 1} \right)\left( { - 2} \right)}&{3\left( 0 \right) + \left( { - 1} \right)\left( 1 \right)} \end{array}} \right)$

AB = $\left( {\begin{array}{*{20}{c}} { - 1}&2 \\ {11}&{ - 1} \end{array}} \right)$ A2 N3

[3 marks]

Examiners’ report

[N/A]