jee-main 2018 Q79

jee-main · India · 15apr_shift1 Simultaneous equations

Let $S$ be the set of all real values of $k$ for which the system of linear equations
$$\begin{aligned} & x + y + z = 2 \\ & 2 x + y - z = 3 \\ & 3 x + 2 y + k z = 4 \end{aligned}$$
has a unique solution. Then $S$ is
(1) an empty set
(2) equal to $\mathrm { R } - \{ 0 \}$
(3) equal to $\{ 0 \}$
(4) equal to $R$

Let $S$ be the set of all real values of $k$ for which the system of linear equations

$$\begin{aligned}
& x + y + z = 2 \\
& 2 x + y - z = 3 \\
& 3 x + 2 y + k z = 4
\end{aligned}$$

has a unique solution. Then $S$ is\\
(1) an empty set\\
(2) equal to $\mathrm { R } - \{ 0 \}$\\
(3) equal to $\{ 0 \}$\\
(4) equal to $R$

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