How many solutions does the system $x + y + z = 2$, $2x + 2y + 2z = 5$, $x - y + z = 1$ have?

Explanation

1. 01

   The first two rows of coefficients are proportional, so $|A| = 0$ and there is no unique solution.

2. 02

   $(\operatorname{adj} A)B = \begin{bmatrix}-2 \\ 0 \\ 2\end{bmatrix} \ne O$, so the system is inconsistent. Directly: the second equation says $x + y + z = \frac{5}{2}$, the first says 2.