I'm having trouble solving a linear equations system with an unknown coefficient. I am trying to solve it using the reduce row echelon form, but to no avail.
x + y + 7z = -7
2x + 3y + 17z = -16
x + 2y + (k2 + 1)z = 3k
[ 1 1 7 | -7 ]
[ 2 3 17| -16]
[ 1 2 k2+1| 3k ]
Specifically, I am trying to simplify this equation to find:
a) no solution "inconsistent"
b) infinite number of solutions "consistent"
c) one solution "unique"
Right now I am just attempting a. I believe I have accidentally already solved c.
So following the procedure...
I subtract 2R1 from R2, giving in the second row:
[ 0 1 3 | -2 ]
I then subtract R1 from R3 giving in the third row:
[ 0 1 k2-6 | 3k+7 ]
Then subtracting R2 from R3 to give:
[ 0 0 k2-9 | 3k+9 ]
From here I am lost. My intuition tells me that 3rd row should simplify to something like this (x representing a non-zero value):
[ 0 0 0 | x ]
Any help would be greatly appreciated.