EXM.1.AHL.TZ0.22

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

Let A = $\left( {\begin{array}{*{20}{c}} 1&x&{ - 1} \\ 3&1&4 \end{array}} \right)$ and B = $\left( {\begin{array}{*{20}{c}} 3 \\ x \\ 2 \end{array}} \right)$ .

Find AB.

[3]

The matrix C = $\left( {\begin{array}{*{20}{c}} {20} \\ {28} \end{array}} \right)$ and 2AB = C. Find the value of $x$ .

[3]

Markscheme / solution

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

Attempting to multiply matrices (M1)

$\left( {\begin{array}{*{20}{c}} 1&x&{ - 1} \\ 3&1&4 \end{array}} \right)\left( {\begin{array}{*{20}{c}} 3 \\ x \\ 2 \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {3 + {x^2} - 2} \\ {9 + x + 8} \end{array}} \right)\left( { = \left( {\begin{array}{*{20}{c}} {1 + {x^2}} \\ {17 + x} \end{array}} \right)} \right)$ A1A1 N3

[3 marks]

Setting up equation M1

eg $2\left( {\begin{array}{*{20}{c}} {1 + {x^2}} \\ {17 + x} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {20} \\ {28} \end{array}} \right)$ , $\left( {\begin{array}{*{20}{c}} {2 + 2{x^2}} \\ {34 + 2x} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {20} \\ {28} \end{array}} \right)$ , $\left( {\begin{array}{*{20}{c}} {1 + {x^2}} \\ {17 + x} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} {10} \\ {14} \end{array}} \right)$

$\begin{array}{*{20}{c}} {2 + 2{x^2} = 20} \\ {34 + 2x = 28} \end{array}\,\,\,\,\,\,\left( {\begin{array}{*{20}{c}} {1 + {x^2} = 10} \\ {17 + x = 14} \end{array}} \right)$ (A1)

$x = - 3$ A1 N2

[3 marks]

Examiners’ report

[N/A]