jee-main 2020 Q62

jee-main · India · session2_05sep_shift2 Matrices Linear System and Inverse Existence

If the system of linear equations $$x + y + 3z = 0$$ $$x + 3y + k^2z = 0$$ $$3x + y + 3z = 0$$ has a non-zero solution $(x, y, z)$ for some $k \in \mathrm{R}$, then $x + \left(\frac{y}{z}\right)$ is equal to:
(1) $-3$
(2) $9$
(3) $3$
(4) $-9$

If the system of linear equations
$$x + y + 3z = 0$$
$$x + 3y + k^2z = 0$$
$$3x + y + 3z = 0$$
has a non-zero solution $(x, y, z)$ for some $k \in \mathrm{R}$, then $x + \left(\frac{y}{z}\right)$ is equal to:\\
(1) $-3$\\
(2) $9$\\
(3) $3$\\
(4) $-9$

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