Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions. x + 2y – 3z = 4 3x – y + 5z = 2 4x + y +(a– 14)z = a +2

The system has solution when:

The system has no solution when:

Step-by-step explanation:

First rewrite the system in its augmented matrix form

Let´s apply row reduction process to  its associated augmented matrix:

Now we have this:

We can conclude now:

The system has no solution when:

And the system has solution when:

b

step-by-step explanation:

the word superfluous means unnecessary