Encontre o determinante da matriz F = 6x6 através do Cálculo de Cofatores e Teorema de Laplace. Ja fiz minha resposta mas quer conferir. Se alguem tiver tempo e estiver disposto. obrii
F=
(1 0 2 1 3 1)
(1 1 2 3 1 0)
(1 0 7 1 3 0)
(1 1 5 3 1 0)
(1 0 4 1 3 0)
(1 1 1 3 1 0)
F=
(1 0 2 1 3 1)
(1 1 2 3 1 0)
(1 0 7 1 3 0)
(1 1 5 3 1 0)
(1 0 4 1 3 0)
(1 1 1 3 1 0)
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1 0 2 1 3 1
1 1 2 3 1 0
1 0 7 1 3 0
1 1 5 3 1 0
1 0 4 1 3 0
1 1 1 3 1 0
L2=L2-L1
L3=L3-L1
L4=L4-L1
L5=L5-L1
L6=L6-L1
1 0 2 1 3 1
0 1 0 2 -2 -1
0 0 5 0 0 -1
0 1 3 1 3 1
0 0 2 0 0 -1
0 1 -1 2 -2 -1
L3=L3-L2
1 0 2 1 3 1
0 1 0 2 -2 -1
0 0 5 0 0 -1
0 0 3 -1 5 2
0 0 2 0 0 -1
0 0 -1 0 0 0
L3=L3+5L6
L4=L4+3L6
L5=L5+2L6
1 0 2 1 3 1
0 1 0 2 -2 -1
0 0 0 0 0 -1
0 0 0 -1 5 2
0 0 0 0 0 -1
0 0 -1 0 0 0
L2=L2+2L4
1 0 2 1 3 1
0 1 0 0 8 3
0 0 0 0 0 -1
0 0 0 -1 5 2
0 0 0 0 0 -1
0 0 -1 0 0 0
det = (-1)¹⁺¹ * 1 * det B
B=
1 0 0 8 3
0 0 0 0 -1
0 0 -1 5 2
0 0 0 0 -1
0 -1 0 0 0
det B = (-1)¹⁺¹ * 1 * det C
C=
0 0 0 -1
0 -1 5 2
0 0 0 -1
-1 0 0 0
det C = (-1)⁴⁺¹ *(-1) * det D
D=
0 0 -1
-1 5 2
0 0 -1
det D = (-1)²⁺¹ *(-1) * det E
E=
0 -1
0 -1
det E = 0
det = (-1)¹⁺¹ * 1 * (-1)¹⁺¹ * 1 * (-1)⁴⁺¹ *(-1) * det E
det = (-1)¹⁺¹ * 1 * (-1)¹⁺¹ * 1 * (-1)⁴⁺¹ *(-1) * 0
det = 0