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9 MATRIISIN ASTE Riviavaruus Vastaavasti kuten matriisin A Rm n ...

9 MATRIISIN ASTE Riviavaruus Vastaavasti kuten matriisin A Rm n ...

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Matematiikka P2 © J.T. Tanttu 25.11.2008 Mat 9-7<br />

TTY, Pori<br />

Lisää tuloksia <strong>matriisin</strong> asteelle<br />

Lause 9.3 Matriisin aste teoreema<br />

Matriisille A !! m"n pätee<br />

rank(A) + dim(Nul(A)) = n<br />

" 1 0 ! 0 0 ! ! !%<br />

$<br />

0 1 ! 0 0 ! ! !<br />

'<br />

$<br />

'<br />

$ " " " " " " '<br />

$<br />

'<br />

$<br />

0 0 ! 0 1 ! ! !<br />

'<br />

$ 0 0 ! 0 0 0 ! 0'<br />

$<br />

'<br />

$ " " " " " " '<br />

# $ 0 0 ! 0 0 0 ! 0&<br />

'

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