QJEEM21Mac40b: JEE Main 2021 Mathematics - Class 12 JEEM21Mac40b Solution: The system of equations kx + y + z = 1, x + ky + z = k and x +…

Question

Verified Solution • 2025–26 Session moderate

The system of equations kx + y + z = 1, x + ky + z = k and x + y + zk = k² has no solution if k is equal to :

Accepted Answer

D = | \begin{matrix} k & 1 & 1 \\ 1 & k & 1 \\ 1 & 1 & k \end{matrix} | = 0

\Rightarrow k (k^{2} - 1) - (k - 1) + (1 - k) = 0

\Rightarrow (k - 1) (k^{2} + k - 1 - 1) = 0

\Rightarrow (k - 1) (k^{2} + k - 2) = 0

\Rightarrow (k - 1) (k - 1) (k + 2) = 0

\Rightarrow k = 1, k = - 2

for k = 1 equation identical so k =

-

2 for no solution.

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