- #1

- 880

- 0

I have the following system of linear equations -

kx + 3y -z = 1

x + 2y - z = 2

-kx + y + 2z = -1

I have reduced it to

1 2 -1 : 2

0 1 1/4 : 0

0 0 (7-6k)/7k : (8-4k)/7

assuming k ≠ 0.

I would now like to be able to determine for what values of k will the system have no solutions, a single solution, and an infinite number of solutions.

Would it be correct to say that there would be no solution for k=7/6, and a single solution for every k ≠ 7/6 (therefore, the system will never have an infinite number of solutions)?