EXM.1.AHL.TZ0.7

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

Let $\left( {\begin{array}{*{20}{c}} b&3 \\ 7&8 \end{array}} \right) + \left( {\begin{array}{*{20}{c}} 9&5 \\ { - 2}&7 \end{array}} \right) = \left( {\begin{array}{*{20}{c}} 4&8 \\ a&{15} \end{array}} \right)$ .

Write down the value of $a$ .

[1]

a.i.

Find the value of $b$ .

[2]

a.ii.

Let $3\left( {\begin{array}{*{20}{c}} { - 4}&8 \\ 2&1 \end{array}} \right) - 5\left( {\begin{array}{*{20}{c}} 2&0 \\ q&{ - 4} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} { - 22}&{24} \\ 9&{23} \end{array}} \right)$ .

Find the value of $q$ .

[3]

Markscheme / solution

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

$a$ = 5 A1 N1

[1 mark]

a.i.

$b$ + 9 = 4 (M1)

$b$ = −5 A1 N2

[2 marks]

a.ii.

Comparing elements 3(2) − 5( $q$ ) = −9 M1

$q$ = 3 A2 N2

[3 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]