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detrminar la matriz de cofactores de una matriz

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Created on March 24, 2026

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Sea A = [[1, 2, 3], [4, 5, 6], [7, 8, 9]] Determinar la matriz de cofactores de A

1. Calcular el menor de cada elemento - M_11 = det([[5, 6], [8, 9]]) = (5_9 - 6_8) = (45 - 48) = -3 - M_12 = det([[4, 6], [7, 9]]) = (4_9 - 6_7) = (36 - 42) = -6 - M_13 = det([[4, 5], [7, 8]]) = (4_8 - 5_7) = (32 - 35) = -3 - M_21 = det([[2, 3], [8, 9]]) = (2_9 - 3_8) = (18 - 24) = -6 - M_22 = det([[1, 3], [7, 9]]) = (1_9 - 3_7) = (9 - 21) = -12 - M_23 = det([[1, 2], [7, 8]]) = (1_8 - 2_7) = (8 - 14) = -6 - M_31 = det([[2, 3], [5, 6]]) = (2_6 - 3_5) = (12 - 15) = -3 - M_32 = det([[1, 3], [4, 6]]) = (1_6 - 3_4) = (6 - 12) = -6 - M_33 = det([[1, 2], [4, 5]]) = (1_5 - 2_4) = (5 - 8) = -3

2. Calcular el cofactor de cada elemento - C_11 = (+) * M_11 = +1 * (-3) = -3 - C_12 = (-) * M_12 = -1 * (-6) = 6 - C_13 = (+) * M_13 = +1 * (-3) = -3 - C_21 = (-) * M_21 = -1 * (-6) = 6 - C_22 = (+) * M_22 = +1 * (-12) -12 - C_23 = (-) * M_23 = -1 * (-6) = 6 - C_31 = (+) * M_31 = +1 * (-3) = -3 - C_32 = (-) * M_32 = -1 * (-6) = 6 - C_33 = (+) * M_33 = +1 * (-3) = -3