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Summary Matemàtiques per la selectivitat
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Matemàtiques explicades amb exemples i molt dinàmicament. Puntuació estudiant d'aquests apunts: 9.
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MATESSELECTIVITAT
,UNITAT 1, 2: MATRIUS I DETERMINANTS
DEFINICIONS
DIMENSIÓ DE LA MATRIU
↳ nº de files que té la matriu x nº de columnes
TIPUS DE MATRIUS
➔ MATRIU QUADRADA: té el mateix nº de files que de columnes
Ex: 2 x 2, 3 x 3, 5 x 5, 6 x 6 …
➔ MATRIU TRIANGULAR (ha de ser una matriu quadrada)
◆ Superior: per sota la diagonal tot 0.
◆ Inferior: per damunt de la diagonal tot 0.
, ➔ MATRIU D’IDENTITAT (ha de ser una matriu quadrada)
A la diagonal té 1 i a la resta tot 0.
➔ MATRIU TRANSPOSADA: passar de columnes a files o viceversa.
OPERACIONS AMB MATRIUS
⚠️
SUMAR I RESTAR
Per sumar o restar una matriu han de tenir la mateixa dimensió!!
(2x2, 2x3…)
Propietats de la suma:
- És commutativa
A+B=B+A
- Perquè un resultat quedi igual, se li ha de sumar un element
neutre, en aquest cas és una matriu neutra, tota de 0.
- Associativa (pots posar parèntesis on vulguis, que no afecta)
(A + B) + C = A + (B + C)
⚠️
MULTIPLICACIÓ
Perquè dos matrius és puguin multiplicar, ha de ser igual el nº de
columnes de la primera matriu amb el nº de files de la segona matriu.
nº de columnes 1a matriu = nº files 2na matriu
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