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The number of real values of λ , such that the system of linear equations

2x – 3y + 5z = 9

x + 3y – z = 18

3x – y (λ2−|λ|)z=16 has no solutions, is

Option 1 -

0

Option 2 -

1

Option 3 -

2

Option 4 -

4

0 2 Views | Posted 2 months ago
Asked by Shiksha User

  • 1 Answer

  • P

    Answered by

    Payal Gupta | Contributor-Level 10

    2 months ago
    Correct Option - 3


    Detailed Solution:

    System of equation can be written as

    (2−3513−13−1λ2−|λ|) (xyz)= (9−1816)

    for no solution

    910 (λ2−|λ|+3)−7=0

    ⇒9λ2−9|λ|−43=0

    ⇒|λ|=9+81+36×4318>0

    ∴ only two possible value of λ are there.

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