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[ROOT]/includes/functions.php:3903) [phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5284: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3903) [phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5284: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3903) Matrice associata rispetto alle basi canoniche ? -Forum Studenti
Forum Studenti
Sito dedicato agli studenti dei corsi tenuti da Massimo Gobbino and friends (qualunque corso può essere aggiunto)
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Ciao a tutti. A breve ho l'esame di algebra lineare e non riesco proprio a capire come risolvere il punto 1 dell'esercizio che ho messo in allegato. Qualche buon'anima mi spiegherebbe come si fa? Grazie in anticipo.
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prova a dare un'occhiata agli esercizi risolti postati qui nella sezione "Algebra lineare" sotto la dicitura "Applicazioni lineari", ci dovrebbero essere almeno 5 schede con esempi risolti oltre a discussioni sui metodi
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f(v₁)=v₂=1e₁+1e₂+0e₃ f(v₂)=v₃=0e₁+0e₂+1e₃ f(v₃)=v₂+v₃=1e₁+1e₂+1e₃ Esprimiamo la trasposta della matrice dei coefficienti (1...0...1) (1...0...1)=B (0...1...1)
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Scusa avevi ragione. Ho provato ad utilizzare un altro metodo per la risoluzione, ovvero mi ricavo la f(e1), f(e2), f(e3) attraverso procedimenti diversi ed il risultato viene uguale al tuo. Grazie ancora!
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Per verificare che l'insieme forma una base di ci basta verificare che il rango della matrice che ha per colonne i tre vettori ha rango massimo. Questo si fa facilmente con il calcolo del determinante (che viene ) oppure con la semplice riduzione a scala secondo l'algoritmo di Gauss.
Sapendo che abbiamo che
è proprio la matrice che stiamo cercando. E credo che da qui sia semplice terminare gli altri punti. Per il calcolo del rango puoi procedere senza problemi con l'algoritmo di Gauss che ti riduce la matrice a scalini.
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