Ok, I'm supposed to determine the values of a for which the system has no solution, exactly one solution, or infinitely many solutions...

The system is:

x+y+7z=-7

2x+3y+17z=-16

x+2y+(a^2+1)z= 3a

So, I would have a matrix of

1 1 7 -7

2 3 17 -16

1 2 (a^2+1) 3a

I'm not sure how to solve for the system from this point using elementary row operations when it comes down to the a values...