JEE Main 2015MathematicsDeterminantsMediumMCQ

JEE Main 2015 — Determinants Question with Solution

JEE Main 2015 (04 Apr)

Question

The set of all values of λ for which the system of linear equations:
2 x 1 - 2 x 2 + x 3 = λ x 1
2 x 1 - 3 x 2 + 2 x 3 = λ x 2
- x 1 + 2 x 2 = λ x 3
has a non-trivial solution,

Choose an option

Show full solutionCorrect option: D
Correct answer
DContains two elements.

Step-by-step explanation

2 - λ x 1 - 2 x 2 + x 3 = 0

2 x 1 - λ + 3 x 2 + 2 x 3 = 0

- x 1 + 2 x 2 - λ x 3 = 0

The systems of linear equations will have a non-trivial solution

⇒     2 - λ - 2 1 2 - λ - 3 2 - 1 2 - λ = 0

⇒     2 - λ λ 2 + 3 λ - 4 + 2 - 2 λ + 2 + 1 4 - λ - 3 = 0

2 λ 2 + 6 λ - 8 - λ 3 - 3 λ 2 + 4 λ - 4 λ + 4 + 1 - λ = 0

- λ 3 - λ 2 + 5 λ - 3 = 0

λ 3 + λ 2 - 5 λ + 3 = 0

λ - 1 λ 2 + 2 λ - 3 = 0

λ - 1 λ + 3 λ - 1 = 0

⇒    λ = -3 , 1 , 1

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About this question

This is a previous-year question from JEE Main 2015, covering the Determinants chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.