enter image description hereSo i have the system of equations as attached on the image above. I want to find the values of k for which the system is consistent.
I put it in the form of an augmented matrix to get
1 1 -1 2
1 1 0 1
1 1 k 0
And if now i put it in row echelon form , i get
1 1 -1 2
0 0 1 -1
0 0 0 1
The k disappears. The system is inconsistent in the last row because z(=0)=1, which is impossible. However, I want to find the values of k for which the system is consistent! How do i do that ?
I don't know how you got that row echelon form, but note that it follows from the second equation that $x+y=1$. So, the first and the third equations become $-z=1$ and $kz=-1$. Obviously, there's one and only one $k$ for which this system is consistent.