The set of equations a + b - 2c = 0 , 2a - 3b + c = 0 , and a - 5b + 4c = α is consistent. If the cofactors of the coefficient matrix A are C_11 = 7, - Mathematics MCQ Mathematics Mock Test - 5 2026 | ExamTest.live

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The set of equations a + b - 2 c = 0, 2 a - 3 b + c = 0, and a - 5 b + 4 c = α is consistent. If the cofactors of the coefficient matrix A are C_{11} = 7, C_{12} = - 7, C_{13} = 7, C_{21} = 6, C_{22} = - 6, C_{23} = 6, C_{31} = 5, C_{32} = - 5, C_{33} = 5, find the value of α .

Solution & Step-by-step Explanation

The system is A X = B where A = 121 1 - 3 - 5 - 2 14 and B = 00 α .Check det (A) : det (A) = 1 (- 12 + 5) - 1 (8 - 1) - 2 (- 10 + 3) = - 7 - 7 + 14 = 0 Since det (A) = 0, for the system to be consistent, (adj A) B must be 0 . adj A = Cofactor Matrix^{T} : adj A = 7 - 7 7 6 - 6 6 5 - 5 5 Multiplying by B : 7 - 7 7 6 - 6 6 5 - 5 5 00 α = 5 α - 5 α 5 α For this to be 000, we must have 5 α = 0 ⟹ α = 0 .

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The set of equations a + b - 2 c = 0, 2 a - 3 b + c = 0, and a - 5 b + 4 c = α is consistent. If the cofactors of the coefficient matrix A are C_{11} = 7, C_{12} = - 7, C_{13} = 7, C_{21} = 6, C_{22} = - 6, C_{23} = 6, C_{31} = 5, C_{32} = - 5, C_{33} = 5, find the value of α .

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