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X - FIIT STU

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Systém lineárnych rovníc<br />

Systém lineárnych rovníc, ktorý obsahuje m rovníc o n neznámych<br />

a11x1 + a12 x<br />

2<br />

+ ... + a1 nxn<br />

= b1<br />

a21x1 + a22x 2<br />

+ ... + a2nxn<br />

= b2<br />

........................................<br />

a x + a x + ... + a x = b<br />

m1 1 m2 2<br />

mn n m<br />

Zavedením matíc<br />

⎛a11 a<br />

12<br />

... a1 n ⎞ ⎛x1 ⎞ ⎛b1<br />

⎞<br />

⎜<br />

a21 a<br />

22<br />

... a<br />

⎟ ⎜<br />

2n<br />

x<br />

⎟ ⎜<br />

2<br />

b<br />

⎟<br />

2<br />

A= ⎜ ⎟, x = ⎜ ⎟,<br />

b = ⎜ ⎟<br />

⎜ ... ... ... ... ⎟ ⎜... ⎟ ⎜ ... ⎟<br />

⎜ ⎟ ⎜ ⎟ ⎜ ⎟<br />

a a ... a x b<br />

⎝ m1 m2<br />

mn⎠ ⎝ n⎠ ⎝ m⎠<br />

Priesvitka 2

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