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Algebra Lineal MATRICES Y DETERMINANTES

Enviado por   •  14 de Octubre de 2018  •  678 Palabras (3 Páginas)  •  563 Visitas

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C22= (2)+(4)= [pic 112][pic 113][pic 114]

A=[pic 115]

EJERCICIO

Sumar el cuadrado de una matriz y su inversa y determinar o hallar

+ [pic 116][pic 117]

= [pic 118][pic 119]

C11=(1)(1)+(-5)(3)=1-15=-14

C12=(1)(-5)+(-5)(-1)=-5+5=0

C21=(3)(1)+(-1)(3)=3-3=0

C22=(3)(5)+(-1)(-1)=-15+1=-14

= [pic 120][pic 121][pic 122]

F2-3F1=F2

3-3(1)=3-3=0

-1-3(-5)=-1+15=14

0-3(1)=0-3=-3

1-3(0)=1-0=1

= [pic 123][pic 124][pic 125]

-14F1-5F2=F1

-14(1)-5(0)=-14-0=-14

-14(-5)-5(14)=70 -70=0

-14(1)-5(-3)=-14+15=1

-14(0)-5(1)=-0 -5=-5

= [pic 126][pic 127][pic 128]

A= [pic 129]

I2 [pic 130]

+ [pic 131][pic 132]

+ [pic 133][pic 134][pic 135]

COFACTORES

A== A’= [pic 136][pic 137][pic 138]

A== (3)(4)-(2)(1)=12-2=10[pic 140][pic 141][pic 139]

-? 2x2= orden[pic 142]

= = = [pic 143][pic 144][pic 145][pic 146][pic 147]

A== (1)(-1)-(-5)(3)= -1+15=14[pic 148]

= = [pic 149][pic 150][pic 151]

INVERSA DE LA MATRIZ

SISTEMA DE 3X3 POR METODO DE GAUS

EJERCICIO 1

[pic 152]

Celdas: 31, 21, 32, 13, 23, 12

2F3+ F1= F3

2(-1)+(2)= -2+2=0

2(0)+(1)= 0+1=1

2(1)+(-2)= 2-2=0

2(0)+(1)= 0+1=1

2(0)+(0)= 0+0=0

2(1)+(0)= 2+0=2

[pic 153]

-2F2+ F1= F2

-2(1)+(2)= -2+2=0

-2(1)+(1)= -2+1= -1

-2(-2)+(-2)= 4-2=2

-2(0)+(1)= 0+1=1

-2(1)+(0)= -2+0= -2

-2(0)+(1)= 0+0=0

[pic 154]

F3+ F2= F3

0+(0)=0+0=0

1+(-1)=1-1=0

0+(2)=0+2=2

1+(1)=1+1=2

0+(-2)=0-2= -2

2+(0)=2+0=2

[pic 155]

F1+ F3= F1

2+(0)=2+0=2

1+(0)=1+0=1

-2+(2)=-2+2=0

1+(2)=1+2=3

0+(-2)=0-2= -2

0+(2)=0+2=2

[pic 156]

F2- F3= F2

0-0=0

-1-0= -1

2-2=0

1-2= -1

-2+2=0

0-2=-2

[pic 157]

F1+ F2= F1

2+0=2

1+(-1)=0

0+0=0

3+(-1)=2

-2+0=-2

2+(-2)=0

÷

÷ [pic 158][pic 159]

[pic 160]

[pic 161][pic 162]

2(1)+ 1(1)+(-2)(1)=1

2(-1)+1(0)+(-2)(-1)=0

2(0)+1(2)+(-2)(1)=0

1(1)+1(1)+(-2)(1)=0

1(-1)+1(0)+(-2)(-1)=1

1(0)+1(2)+(-2)(1)=0

-1(1)+0(1)+1(1)=0

-1(-1)+0(0)+1(-1)=0

-1(0)+0(2)+1(1)=1

[pic 163]

EJERCICIO 2 TERMINAR

A1= [pic 164]

C=31, 21, 32, 13, 23, 12

3F3+F1=F3

3(-1)+3=0

3(2)+2=8

3(1)+5=8

3(0)+1=1

3(0)+0=0

3(1)+0=3

A2=[pic 165]

3F2-2F1=F2

3(2)-2(3)=0

3(-1)-2(2)=-7

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