jee-main 2021 Q68

jee-main · India · session1_26feb_shift2 Matrices Linear System and Inverse Existence
Consider the following system of equations: $$\begin{aligned} & x + 2 y - 3 z = a \\ & 2 x + 6 y - 11 z = b \\ & x - 2 y + 7 z = c \end{aligned}$$ where $a , b$ and $c$ are real constants. Then the system of equations :
(1) has a unique solution when $5 a = 2 b + c$
(2) has no solution for all $a , b$ and $c$
(3) has infinite number of solutions when $5 a = 2 b + c$
(4) has a unique solution for all $a , b$ and $c$
Consider the following system of equations:
$$\begin{aligned}
& x + 2 y - 3 z = a \\
& 2 x + 6 y - 11 z = b \\
& x - 2 y + 7 z = c
\end{aligned}$$
where $a , b$ and $c$ are real constants. Then the system of equations :\\
(1) has a unique solution when $5 a = 2 b + c$\\
(2) has no solution for all $a , b$ and $c$\\
(3) has infinite number of solutions when $5 a = 2 b + c$\\
(4) has a unique solution for all $a , b$ and $c$