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The set of all values of l for which the system of linear equations
2x1 - 2x2 + x3 = λx1
2x1 - 3x2 + 2x3 = λx2
-x1 + 2x2  = λx3
has a non-trivial solution
  • a)
    Is an empty set
  • b)
    Is a singleton
  • c)
    Contains two elements
  • d)
    Contains more than two elements
Correct answer is option 'C'. Can you explain this answer?
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The set of all values of l for which the system of linear equations2x1...
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The set of all values of l for which the system of linear equations2x1...
x1(2 - λ) - 2x2 + x3 = 0
2x1 +x2(-λ - 3) + 2x3 = 0

(2 - λ)(λ2 + 3λ- 4)+ 2(-2λ + 2)+(4 - λ- 3) = 0
+ 6λ - 8 - λ3 - 3λ2 + 4λ - 4λ + 4 -λ + 1 =0

=> λ = 1, 1, -3
Two elements.
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The set of all values of l for which the system of linear equations2x1 - 2x2 + x3 = λx12x1 - 3x2 + 2x3 = λx2-x1 + 2x2 = λx3has a non-trivial solutiona)Is an empty setb)Is a singletonc)Contains two elementsd)Contains more than two elementsCorrect answer is option 'C'. Can you explain this answer?
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The set of all values of l for which the system of linear equations2x1 - 2x2 + x3 = λx12x1 - 3x2 + 2x3 = λx2-x1 + 2x2 = λx3has a non-trivial solutiona)Is an empty setb)Is a singletonc)Contains two elementsd)Contains more than two elementsCorrect answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about The set of all values of l for which the system of linear equations2x1 - 2x2 + x3 = λx12x1 - 3x2 + 2x3 = λx2-x1 + 2x2 = λx3has a non-trivial solutiona)Is an empty setb)Is a singletonc)Contains two elementsd)Contains more than two elementsCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The set of all values of l for which the system of linear equations2x1 - 2x2 + x3 = λx12x1 - 3x2 + 2x3 = λx2-x1 + 2x2 = λx3has a non-trivial solutiona)Is an empty setb)Is a singletonc)Contains two elementsd)Contains more than two elementsCorrect answer is option 'C'. Can you explain this answer?.
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