Examine the consistency of the system of equations.

x + y + z = 1

2x + 3y + 2z = 2

ax + ay + 2az = 4

The given system of equations is:

x + y + z = 1

2x + 3y + 2z = 2

ax + ay + 2az = 4

The given system of equations can be written in the form of AX = B, where

Now |A| = 1(6a-2a)-1(4a-2a) +1(2a-3a) = a ≠ 0

∴ A is a non-singular matrix and hence A^-1 exists.

So the system of equations will be consistent.