EXM.1.AHL.TZ0.52

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

Find the inverse of the matrix $\left( {\begin{array}{*{20}{c}} 1&2&1 \\ 1&1&2 \\ 2&1&4 \end{array}} \right)$ .

[2]

Hence solve the system of equations

$x + 2y + z = 0$

$x + y + 2z = 7$

$2x + y + z = 17$

[4]

Markscheme / solution

${\left( {\begin{array}{*{20}{c}} 1&2&1 \\ 1&1&2 \\ 2&1&4 \end{array}} \right)^{ - 1}} = \left( {\begin{array}{*{20}{c}} 2&{ - 7}&3 \\ 0&2&{ - 1} \\ { - 1}&3&{ - 1} \end{array}} \right)$ A2 N2

[2 marks]

In matrix form A $x$ = B or $x$ = A⁻¹ B M1

$x = 2$ , $y = -3$ , $z = 4$ A1A1A1 N0

[4 marks]

Examiners’ report

[N/A]