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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{aligne…

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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:

[JEE Main 2021, 26 Feb (Shift 2)]

a

\(\text { Has no solution for all } a, b \text { and } c\)

b

\(\text { Has a unique solution when } 5 a=2 b+c\)

c

\(\text { Has infinite number of solutions when } 5 a=2 b+c\)

d

\(\text { Has a unique solution for all } a, b \text { and } c\)

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