QJEEM21Ma038a: JEE Main 2021 Mathematics - Class 12 JEEM21Ma038a Solution: Let [ λ ] be the greatest integer less than or equal to λ . The …

Question

Verified Solution • 2025–26 Session moderate

Let [

λ

] be the greatest integer less than or equal to

λ

. The set of all values of

λ

for which the system of linear equations
x + y + z = 4,
3x + 2y + 5z = 3,
9x + 4y + (28 + [

λ

])z = [

λ

] has a solution is :

Accepted Answer

D = | \begin{matrix} 1 & 1 & 1 \\ 3 & 2 & 5 \\ 9 & 4 & 28 + [λ] \end{matrix} | = - 24 - [λ] + 15 = - [λ] - 9

if

[λ] + 9 \neq 0

then unique solution

if

[λ] + 9 = 0

then D₁ = D₂ = D₃ = 0

so infinite solutions

Hence,

λ

can be any red number.

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