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Web skærmformat. - Aarhus Universitet

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V. Matricer – 4. Determinanter 434<br />

Dette giver løsninger ⎛<br />

⎝<br />

x1<br />

x2<br />

x3<br />

⎞ ⎛ ⎞<br />

−1<br />

⎛ ⎞<br />

−1<br />

⎠ = x2 ⎝ 1 ⎠ + x3 ⎝ 0 ⎠<br />

0 1<br />

4.30. Test entydig løsning ☞ [LA] 8 Determinanter<br />

Test<br />

⎛<br />

−1 a<br />

⎞<br />

−1<br />

Gælder der altid, at alle ligningssystemer med koefficientmatrix ⎝ 0 1 b ⎠ har en entydig<br />

0<br />

løsning.<br />

0 2<br />

Afkryds:<br />

ja<br />

<br />

nej<br />

Løsning <br />

−1<br />

0<br />

0<br />

a<br />

1<br />

0<br />

<br />

−1<br />

<br />

b <br />

= (−1) · 1 · 2 = −2 = 0<br />

2

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