The value of `|alpha|` for which the system of equation `alphax+y+z=alpha-1` `x+alphay+z=alpha-1` `x+y+alphaz=alpha-1` has no solutions, is ________.

Explanation

To solve the problem, we need to determine the value of \(|\alpha|\) for which the given system of equations has no solutions. The system of equations is:

1. \(\alpha x + y + z = \alpha - 1\)
2. \(x + \alpha y + z = \alpha - 1\)
3. \(x + y + \alpha z = \alpha - 1\)

### Step 1: Write the system in matrix form

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