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8. Determinants d'ordre 2 i 3

La forma més pràctica de calcular un determinant d'ordre 2 o 3 és aplicant la Regla de Sarrus. 

(recordeu que només es pot calcular el determinant d'una matriu quadrada (igual nombre de files que columnes). 

Determinant d'una matriu 2x2

  A equals open parentheses table row a b row c d end table close parentheses      rightwards double arrow    open vertical bar bold A close vertical bar bold equals open vertical bar table row bold a bold b row bold c bold d end table close vertical bar bold equals bold italic a bold times bold italic d bold minus bold italic b bold times bold italic c

  Exemple

  A equals open parentheses table row 2 3 row cell negative 4 end cell 5 end table close parentheses space space space rightwards double arrow space space space open vertical bar A close vertical bar equals 2 times 5 minus 3 times left parenthesis negative 4 right parenthesis equals 10 plus 12 equals 22

 Determinant d'una matriu 3x3  

A equals open parentheses table row cell a subscript 11 end cell cell a subscript 12 end cell cell a subscript 13 end cell row cell a subscript 21 end cell cell a subscript 22 end cell cell a subscript 23 end cell row cell a subscript 31 end cell cell a subscript 32 end cell cell a subscript 33 end cell end table close parentheses space table row cell space space space space space space space space end cell row blank row blank end table             

 open vertical bar A close vertical bar equals open vertical bar table row cell a subscript 11 end cell cell a subscript 12 end cell cell a subscript 13 end cell row cell a subscript 21 end cell cell a subscript 22 end cell cell a subscript 23 end cell row cell a subscript 31 end cell cell a subscript 32 end cell cell a subscript 33 end cell end table close vertical bar equals table row blank row cell a subscript 11 times a subscript 22 times a subscript 33 plus a subscript 21 times a subscript 32 times a subscript 13 plus a subscript 12 times a subscript 23 times a subscript 31 minus end cell row cell negative open square brackets a subscript 31 times a subscript 22 times a subscript 13 plus a subscript 32 times a subscript 23 times a subscript 11 plus a subscript 12 times a subscript 21 times a subscript 33 close square brackets end cell end table

Exemple: 

Calcular el determinant de la matriu open parentheses table row 2 cell negative 1 end cell 3 row 1 cell negative 4 end cell 1 row cell negative 3 end cell 0 1 end table close parentheses

Ho resolem en aquest vídeo on podreu veure més clarament com es calcula:   

     

                    

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