Q78.The set of all values of λ for which the system of linear equations x −2y −2z = λx x + 2y + z = λy −x −y = λz has a non-trivial solution : (1) is an empty set (2) contains more than two elements (3) is a singleton (4) contains exactly two elements
What This Question Tests
The question tests the fundamental condition for a homogeneous system of linear equations to have a non-trivial solution, which involves setting the determinant of the coefficient matrix to zero.
Concepts Tested
Formulas Used
For a homogeneous system Ax=0 to have non-trivial solution, det(A) = 0
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📋 Question Details
- Chapter
- Determinants
- Topic
- System of linear equations (non-trivial solution)
- Year
- 2019
- Shift
- 12 Jan Shift 2
- Q Number
- Q78
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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