Let \(S _1\) and \(S _2\) be respectively the sets of all \(a \in R -\{0\}\) for which the system of linear equations \(…

Let \(S _1\) and \(S _2\) be respectively the sets of all \(a \in R -\{0\}\) for which the system of linear equations \(\begin{aligned}&a x+2 a y-3 a z=1\\ &(2 a+1) x+(2 a+3) y+(a+1) z=2 \\& (3 a+5) x+(a+5) y+(a+2) z=3\end{aligned}\)

has unique solution and infinitely many solutions. Then

[JEE Main 2023, 25 Jan (Shift 1)]