JEE Main 2019MathematicsDeterminantsEasyMCQ

JEE Main 2019 — Determinants Question with Solution

JEE Main 2019 (12 Jan Shift 2)

Question

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 :

Choose an option

Show full solutionCorrect option: C
Correct answer
Cis a singleton

Step-by-step explanation

For non-trivial solution, ∆=0.

⇒1-λ-2-212-λ1-1-1-λ=0

⇒1-λ-2λ+λ2+1+1-λ+1-1 -1+2-λ=0

⇒λ2-3λ2+3λ-1=0

⇒λ-13=0

⇒λ=1

Singleton set

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About this question

This is a previous-year question from JEE Main 2019, 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.