Q78.The set of all values of λ for which the system of linear equations: 2x1 −2x2 + x3 = λx1 2x1 −3x2 + 2x3 = λx2 −x1 + 2x2 = λx3 has a non-trivial solution, (1) Contains more than two elements. (2) Is an empty set. (3) Is a singleton. (4) Contains two elements.
What This Question Tests
This question tests the ability to form a coefficient matrix for a homogeneous system of linear equations and apply the condition for a non-trivial solution, which requires the determinant of the coefficient matrix to be zero.
Concepts Tested
Formulas Used
For a homogeneous system Ax=0, a non-trivial solution exists if det(A) = 0
📚 NCERT Sections This Tests
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📋 Question Details
- Chapter
- Matrices & Determinants
- Topic
- System of Linear Equations
- Year
- 2015
- Shift
- 04 Apr
- Q Number
- Q78
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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