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Let $S_1$ and $S_2$ be respectively the sets of all $a \in R -\{0\}$ for which the system of linear equations

$a x+2 a y-3 a z=1$

$(2 a+1) x+(2 a+3) y+(a+1) z=2$

$(3 a+5) x+(a+5) y+(a+2) z=3$

has unique solution and infinitely many solutions. Then

  • [JEE MAIN 2023]
  • A

    $n \left( S _1\right)=2$ and $S _2$ is an infinite set

  • B

    $S_1$ is an infinite set an $n\left(S_2\right)=2$

  • C

    $S _1=\Phi$ and $S _2= R -\{0\}$

  • D

    $S _1= R -\{0\}$ and $S _2=\Phi$

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