- #1
peripatein
- 880
- 0
Hello,
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)?
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)?