Calculo numerico

AAP II

Instrução 1: Método de Cramer

A= 4 1 1 x = x B= 6 1 6 1 Y 8 2 1 8 Z 11

P P PS S S
A= 4 1 1 4 1 P= (4x6x8) + (1x1x2) + (1x1x1) = 192+2+1= 195 1 6 1 1 6 S=(1x6x2) + (4x1x1) + ( 1x1x8) = 12+4+8 = 24 2 1 8 2 1 Determinante A= 195-24 = 171

P P PS S S
Ax= 6 1 1 6 1 P= (6x6x8) + (1x1x11) + (1x8x1) = 288+11+8 = 307 8 6 1 8 6 S= (1x6x11) + (6x1x1) + (1x8x8) = 66+6+64 = 136 11 1 8 11 1 Determinante Ax= 307-136 = 171

P P PS S S
Ay= 4 6 1 4 6 P= (4x8x8) + (6x1x2) + (1x1x11) = 256+12+11 = 279 1 8 1 1 8 S= (1x8x2) + (4x1x11) + (6x1x8) = 16+44+48 = 108 2 11 8 2 11 Determinante Ay= 279-108= 171

P P PS S S
Az= 4 1 6 4 1 P=(4x6x11) + (1x8x2) + (6x1x1) = 264+16+6 = 286 1 6 8 1 6 S= (6x6x2) + (4x8x1) + (1x1x11) = 72+32+11 =115 2 1 11 2 1 Determinante Az= 286-115= 171
X= determinante Ax/determinante A x= 171/171=1
Y= determinante Ay/determinante A Y=171/171=1
Z=determinante Az/ determinante A z=171/171=1

Portanto x=1, y=1 e z=1

Instrução 2 Método de Gauss

4 1 1 6
1 6 1 8 m1= a21/a11 = ¼ =0,25
2 1 8 11

Novo a21 = a21-m1.a11=1-(0,25x4)=0
Novo a22 = a22-m1.a12=6-(0,25x1)=5,75
Novo a23 = a23-m1.a13=1-(0,25x1)=0,75
Novo a24 = a24-m1.a14=8-(0.,25x6)=6,5

4 1 1 6
0 5,75 0,75 6,5 m2=a31/a11 =2/4