Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y + z = 2, 2x - 2y + 3z = 1, x + 2y - (a2 - 3)z = a

a) If and . The system has no solution

b) If and a different to 2, we have a unique solution.

c) If and we have infinitely solutions.

Step-by-step explanation:

We need to rewrite the third equation in terms of a and z to solve this.

Let's start solving the first equation:

(1)

If we subtract z in both side of this equation we will have:

(2)

Now we can put the equation 2 into the last equation:

(3)

Simplifying the equation 3 we have:

(4)

Now we can analyzes the equation 4 for each case:

a) If and . The system has no solution

b) If and a different to 2, we have a unique solution.

c) If and we have infinitely solutions.

I hope it helps you!