Examine the consistency of the system of equations
`x + y + z = 1`
`2x + 3y + 2z = 2`
`a x + a y + 2a z = 4`

Explanation

To examine the consistency of the given system of equations, we will represent the system in matrix form and calculate the determinant of the coefficient matrix. The system of equations is:

1. \( x + y + z = 1 \)
2. \( 2x + 3y + 2z = 2 \)
3. \( ax + ay + 2az = 4 \)

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

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