Fellesemnet i Matematikk

# Økt 36. Obligatorisk øving

## Fellesemnet i Matematikk

### 36. Økt 36. Obligatorisk øving

Oppgåve 36.1 (Eksamen juni 2014, Del I) Lat

$\begin{array}{llll}\hfill A& =\left[\begin{array}{ccc}\hfill 2\hfill & \hfill 0\hfill & \hfill -1\hfill \\ \hfill 4\hfill & \hfill -5\hfill & \hfill 2\hfill \end{array}\right]\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill B& =\left[\begin{array}{cc}\hfill 1\hfill & \hfill 1\hfill \\ \hfill 1\hfill & \hfill -1\hfill \end{array}\right].\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Om mogleg, rekn ut $AB$ og $BA$.

Oppgåve 36.2 (Eksamen juni 2014, Del I) Finn alle løysingane til likninsystemet

$\begin{array}{llll}\hfill {x}_{1}+2{x}_{2}-{x}_{3}-2{x}_{4}& =1,\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 2{x}_{1}+2{x}_{2}-4{x}_{3}+2{x}_{4}& =0,\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill -{x}_{1}-{x}_{2}+{x}_{3}+{x}_{4}& =1.\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Oppgåve 36.3 (Eksamen november 2012, Del I) Finn alle løysingane til likninsystemet

$\begin{array}{llll}\hfill {x}_{1}+2{x}_{2}-{x}_{3}& =1,\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 5{x}_{1}+9{x}_{2}-3{x}_{3}& =2,\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill 4{x}_{1}+7{x}_{2}-3{x}_{3}& =2.\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Oppgåve 36.4 Lat

$\begin{array}{lll}\hfill A=\left[\begin{array}{ccc}\hfill 1\hfill & \hfill 1\hfill & \hfill 2\hfill \\ \hfill 2\hfill & \hfill -1\hfill & \hfill 0\hfill \\ \hfill 0\hfill & \hfill 1\hfill & \hfill 1\hfill \end{array}\right].& \phantom{\rule{2em}{0ex}}& \hfill \end{array}$

Finn ${A}^{-1}$.

Oppgåve 36.5 (Eksamen juni 2013, Del II) Løys differentiallikninga

$\begin{array}{lll}\hfill {y}^{\prime }=\frac{2y}{x}+{x}^{2}.& \phantom{\rule{2em}{0ex}}& \hfill \end{array}$

Oppgåve 36.6 (Eksamen juni 2014, Del II) Løys differentiallikninga

$\begin{array}{lll}\hfill \frac{dy}{dx}={e}^{-y}cosx.& \phantom{\rule{2em}{0ex}}& \hfill \end{array}$