jee-main 2021 Q67

jee-main · India · session1_24feb_shift2 Matrices Linear System and Inverse Existence

For the system of linear equations: $$x - 2 y = 1 , x - y + k z = - 2 , k y + 4 z = 6 , k \in R$$ Consider the following statements:
(A) The system has unique solution if $k \neq 2 , k \neq - 2$.
(B) The system has unique solution if $k = - 2$.
(C) The system has unique solution if $k = 2$.
(D) The system has no-solution if $k = 2$.
(E) The system has infinitely many solutions if $k = - 2$.

For the system of linear equations:
$$x - 2 y = 1 , x - y + k z = - 2 , k y + 4 z = 6 , k \in R$$
Consider the following statements:\\
(A) The system has unique solution if $k \neq 2 , k \neq - 2$.\\
(B) The system has unique solution if $k = - 2$.\\
(C) The system has unique solution if $k = 2$.\\
(D) The system has no-solution if $k = 2$.\\
(E) The system has infinitely many solutions if $k = - 2$.

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