Q79.The system of linear equations x + λy −z = 0 λx −y −z = 0 x + y −λz = 0 has a non -trivial solution for (1) Exactly two values of λ (2) Exactly three values of λ (3) Infinitely many values of λ (4) Exactly one value of λ
What This Question Tests
This question evaluates the 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 and solving the resulting polynomial equation for the unknown parameter.
Concepts Tested
Formulas Used
det(A) = 0 for non-trivial solutions of Ax=0
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
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12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
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Chemistry Class 11 · Chapter 1
1.1 Define the term solution. How many types of solutions are formed? Write briefly about each type with an example.
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3.23 The rate constant for the decomposition of hydrocarbons is 2.418 × 10–5s–1 at 546 K. If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential factor.
📋 Question Details
- Chapter
- Determinants
- Topic
- Homogeneous system of linear equations
- Year
- 2016
- Shift
- 03 Apr
- Q Number
- Q79
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 4: Determinants
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