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Matemática discreta Exemplos
A=[0.40.20.30.1]A=[0.40.20.30.1]
Etapa 1
The inverse of a 2×22×2 matrix can be found using the formula 1ad-bc[d-b-ca]1ad−bc[d−b−ca] where ad-bcad−bc is the determinant.
Etapa 2
Etapa 2.1
O determinante de uma matriz 2×22×2 pode ser encontrado ao usar a fórmula |abcd|=ad-cb∣∣∣abcd∣∣∣=ad−cb.
0.4⋅0.1-0.3⋅0.20.4⋅0.1−0.3⋅0.2
Etapa 2.2
Simplifique o determinante.
Etapa 2.2.1
Simplifique cada termo.
Etapa 2.2.1.1
Multiplique 0.40.4 por 0.10.1.
0.04-0.3⋅0.20.04−0.3⋅0.2
Etapa 2.2.1.2
Multiplique -0.3−0.3 por 0.20.2.
0.04-0.060.04−0.06
0.04-0.060.04−0.06
Etapa 2.2.2
Subtraia 0.060.06 de 0.040.04.
-0.02−0.02
-0.02−0.02
-0.02−0.02
Etapa 3
Since the determinant is non-zero, the inverse exists.
Etapa 4
Substitute the known values into the formula for the inverse.
1-0.02[0.1-0.2-0.30.4]1−0.02[0.1−0.2−0.30.4]
Etapa 5
Divida 11 por -0.02−0.02.
-50[0.1-0.2-0.30.4]−50[0.1−0.2−0.30.4]
Etapa 6
Multiplique -50−50 por cada elemento da matriz.
[-50⋅0.1-50⋅-0.2-50⋅-0.3-50⋅0.4][−50⋅0.1−50⋅−0.2−50⋅−0.3−50⋅0.4]
Etapa 7
Etapa 7.1
Multiplique -50−50 por 0.10.1.
[-5-50⋅-0.2-50⋅-0.3-50⋅0.4][−5−50⋅−0.2−50⋅−0.3−50⋅0.4]
Etapa 7.2
Multiplique -50−50 por -0.2−0.2.
[-510-50⋅-0.3-50⋅0.4][−510−50⋅−0.3−50⋅0.4]
Etapa 7.3
Multiplique -50−50 por -0.3−0.3.
[-51015-50⋅0.4][−51015−50⋅0.4]
Etapa 7.4
Multiplique -50−50 por 0.40.4.
[-51015-20][−51015−20]
[-51015-20]