11 Matrices (Matriz Inversa)
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Transcript of 11 Matrices (Matriz Inversa)
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Prof. Lic. Javier Velásquez Espinoza
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Dada una matriz “A”, su inversa se denota como: 1A
Definición: IAAAA .. 11
Donde: 0A nAó no singular y
7 3
2 1A
1 3-
2- 7 B BA.
1 0
0 1=
1AB
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MÉTODO PARA ENCONTRAR LA INVERSA DE UNA MATRIZ
nMSi es una Matriz invertible; de:
IM 1MIO.E.
Si una Matriz M no se reduce a I, entonces no existe1M
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Ejemplo 1: Determinar ; si A es invertible.
10 3
6 2A
IA
10 3
6 2A
1
3- 5
23-
1A
121 F
213 FF
123 FF
1AI
1A
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Ejemplo 2: Determinar ; si A es invertible.
1A
10- 2 1
1 2- 4
2- 0 1
A
10- 2 1
1 2- 4
2- 0 1
A IA
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1A
1AI
214 FF
31 FF
221 F
322 FF
132 FF
2329 FF
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Ejemplo 3: Determinar la inversa de:
4 6
2 3A
4 6
2 3A
A no es invertible.
IA
131 F 216 FF
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Pregunta: ¿Para qué me sirve la Matriz Inversa?
Respuesta: Para resolver sistemas de Ecuaciones de dos o más variables e identificar rápidamente un sistema de ecuaciones compatibles indeterminados.
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Del Sistema:
3993
1854
yx
yx
9 3
5- 4
y
x
39
18=
FORMA MATRICIAL
A X B
AX = B BI -1AX BAX 1
=.
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Al Resolver: BAX .1
1 0 9 3
0 1 5- 4 21 FF
131 F 214 FF
2171 F
123 FF
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123 FF
1A 511
4 3-
5 9 = 511
X =
4 3-
5 9
39
18
X =511
=511
102
357
2y 7 x
=
2
7=
y
x++