Q63.Let λ ∈R. The system of linear equations 2x1 −4x2 + λx3 = 1 x1 −6x2 + x3 = 2 λx1 −10x2 + 4x3 = 3 is inconsistent for : (1) exactly one positive value of λ (2) exactly one negative value of λ (3) every value of λ (4) exactly two values of λ
What This Question Tests
This problem tests the conditions for a system of linear equations to be inconsistent, involving calculating the determinant of the coefficient matrix and checking the rank of the augmented matrix using elementary row operations.
Concepts Tested
Formulas Used
System is inconsistent if det(A)=0 and adj(A)⋅B ≠ 0
Gaussian elimination for rank analysis
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📋 Question Details
- Chapter
- Matrices & Determinants
- Topic
- System of linear equations
- Year
- 2020
- Shift
- 05 Sep Shift 1
- Q Number
- Q63
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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