estatista e probabilidade
486 palavras
2 páginas
Cramer 4x + y + z = 6 x + 6y + z = 8
2x + y + 8z = 11
A = 4 1 1 X = x B = 6 1 6 1 y 8 2 1 8 z 11
A = 4 1 1 4 1 1 6 1 1 6 Det A = 192+2+1-12-4-8 2 1 8 2 1 Det A = 171
Ax = 6 1 1 6 1 8 6 1 8 6 Det Ax = 288+11+8-66-6-64 11 1 8 11 1 Det Ax = 171
Ay = 4 6 1 4 6 1 8 1 1 8 Det Ay = 256+12+11-16-44-48 2 11 8 2 11 Det Ay = 171
Az = 4 1 6 4 1 1 6 8 1 6 Det Az = 264+16+6-72-32-11 2 1 11 2 1 Det Az = 171
x = (det Ax) /( det A) x = 171/171 x = 1
y = (det Ax) /( det A) y = 171/171 y = 1
z = (det Ax) /( det A) z = 171/171 z = 1
S = ( 1 , 1 , 1 )
Gauss
4x + y + z = 6 x + 6y + z = 8
2x + y + 8z = 11
4 1 1 6
1 6 1 8 m1 = 1/4
2 1 8 11
1 - 1/4 * (4) = 0
6 - 1/4 * (1) = 23/4
1 - 1/4 * (1) = 3/4
8 - 1/4 * (6) = 13/2
4 1 1 6
0 23/4 3/4 13/2 m2 = (2/4)
2 1 8 11 m2 = 1/2
2 - 1/2 * (4) = 0
1 - 1/2 * (1) = 1/2
8 - 1/2 * (1) = 15/2
11 - 1/2 * (6) = 8
4 1 1 6
0 23/4 3/4 13/2 m3 = (1/2)/(23/4)
0 1/2 15/2 8 m3 = 2/23
0 - 2/23 * (0) = 0
1/2 - 2/23 * (23/4) = 0
15/2 - 2/23 * (3/4) = 171/23
8 - 2/23 * (13/2) = 171/23
4 1 1 6
0 23/4 3/4 13/2
0 0 171/23 171/23
171/23 z = 171/23 z = 1
23/4 y + 3/4 z = 13/2