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Sumario Resumen Determinantes Completo
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DETERMINANTESDETERMINANTES 2X2 DETERMINANTES 3X3 - REGLA DE SARRUS
a b
= ad − bc
c d a b c
d e f = ( a·e·i + b·f·g + d·h·c ) − ( c·e·g + b·d·i + f·h·a )
g h i
PROPIEDADES DE LOS DETERMINANTES
At = A 9 SI UNA MATRIZ TIENE UNA LINEA QUE ES COMBINACION LINEAL
3 1 −1 3 1 −2 DE LAS DEMAS PARALELAS, ENTONCES SU DETERMINANTE ES 0
1 0 2 = 1
−2 5 3 −1
0 5
2 3
1
(Y RECIPROCAMENTE
1a b a+b
1 −2 −1 =0
a·A =an · A SIENDO A UNA MATRIZ DE ORDEN n. 0 3 3
I =1 SI UNA MATRIZ ES INVERTIBLE A −1 = 1
no A
SI UN DETERMINANTE TIENE UNA LINEA l(FILA O COLUMNA)l DE
n EL DETERMINANTE DE UNA MATRIZ TRIANGULAR, ES EL
CEROS, ENTONCES SU DETERMINANTE ES 0
1 0 5 PRODUCTO DE LOS ELEMENTOS DE SU DIAGONAL PRINCIPAL
3 0 2 =0 1 0 0
−2 0 1 −2 2 0 = 6
0 1 3
SI PERMUTAMOS DOS LINEAS DE UNA MATRIZ, SU DETERMINANTE
1 12 SI UNA MATRIZ TIENE DOS LINEAS PROPORCIONALES, SU
CAMBIA DE SIGNO 3 2 −4
2 1 −1 1 2 −1 DETERMINANTE ES 0 (Y VICEVERSA 1 0 2 = 0
−1 0 4 =− 0 −1 4 1 1 6 4 −8
3 3 2 3 3 2
SI UNA MATRIZ TIENE DOS LINEAS IGUALES, SU DETERMINANTE B SI A UNA LINEA DE UNA MATRIZ SE LE SUMA UNA COMBINACION
3 1 3 LINEAL DE OTRAS LINEAS PARALELAS, EL DETERMINANTE NO
ES 0 5 2 5 =0 VARIA 35
q
7 3 7 3 0 −1 3+3·(-1) 0 −1
SI MULTIPLICAMOS CADA ELEMENTO DE UNA LINEA DE UNA 2 3 0 = 2+3·0 3 0 =
−1 4 3 −1+3·3 4 3
MATRIZ POR UN NUMERO, EL DETERMINANTE DE ESA MATRIZ 0 0 -1
QUEDA MULTIPLICADO POR ESE NUMERO =2 3 0
1 −2 3 4 −8 12 8 4 3
4· 1 3 5 = 1 3 5 14 EL DETERMINANTE DE UNA MATRIZ DIAGONAL, ES EL PRODUCTO
0 2 3 0 2 3
DE LOS ELEMENTOS DE SU DIAGONAL PRINCIPAL
SI TODOS LOS ELEMENTOS DE UNA LINEA ESTAN FORMADOS 5 0 0
POR DOS SUMANDOS, DICHO DETERMINANTE SE DESCOMPONE EN
LA SUMA DE DOS DETERMINANTES EN LOS QUE LAS DEMAS
LINEAS PERMANECEN INVARIANTES
0 −1
0 0
es A· B = A · B POR LO QUE
Y 0 = −10
2
An = A n
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