Q70. x + y + z = 4, The values of m, n, for which the system of equations 2x + 5y + 5z = 17, has infinitely many solutions, x + 2y + mz = n satisfy the equation: (1) m2 + n2 −mn = 39 (2) m2 + n2 −m −n = 46 (3) m2 + n2 + m + n = 64 (4) m2 + n2 + mn = 68
What This Question Tests
The question tests the properties of determinants and the relationship between a matrix, its adjoint (matrix of cofactors), and its determinant. It requires careful calculation of determinants and solving for α and β.
Concepts Tested
Formulas Used
A⁻¹ = Adj(A) / det(A)
B = Adj(A)
det(AB) = det(A)det(B)
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Matrices
- Topic
- Cofactor matrix and determinant
- Year
- 2024
- Shift
- 05 Apr Shift 2
- Q Number
- Q70
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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