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X - FIIT STU

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Príklad<br />

Použitím Gaussovej eliminačnej metódy riešte systém<br />

2x − 3x + x = 0<br />

1 2 3<br />

x + 2x − x = 3<br />

1 2 3<br />

2x1+ x2 + x3<br />

= 12<br />

Rozšírená matica má tvar<br />

⎛2 −3 1 0 ⎞<br />

⎜<br />

⎟<br />

A ′ = 1 2 −1 3<br />

⎜2 1 1 12⎟<br />

⎝<br />

⎠<br />

1. krok. Vykonáme vynulovanie prvkov pod diagonálou v prvom stĺpci<br />

⎛2 −3 1 0 ⎞ ⎛2 −3 1 0 ⎞<br />

⎜ ⎟ ⎜ ⎟<br />

1 2 −1 3 ∼ 0 −7 3 −6<br />

⎜2 1 1 12⎟ ⎜0 4 0 12⎟<br />

⎝ ⎠ ⎝ ⎠<br />

Priesvitka 17

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