Let \(A=\left[\begin{matrix}1 & 3 & -1 \\ 2 & 1 & \alpha \\ 0 & 1 & -1\end{matrix}\right]\) be a singular matrix. Let \(…

Let \(A=\left[\begin{matrix}1 & 3 & -1 \\ 2 & 1 & \alpha \\ 0 & 1 & -1\end{matrix}\right]\) be a singular matrix. Let \(f(x)={\int }_{0}^{x}\left({t}^{2}+2t+3\right)dt,x\in [1,\alpha ]\). If \(M\) and \(m\) are respectively be the maximum and the minimum values of \(f\) in \([1,\alpha ]\), then \(3(M-m)\) is equal to:

[JEE Main 2026, 6 Apr (Shift 2)]