Well, the linear system which at least has one solution is called "consistent" linear system.
Find an equation involving g, h, and k that makes
this augmented matrix correspond to a consistent system:
$$\begin{bmatrix}
1 &-4 &7 &g \\
0 & 3 & -5 &h \\
-2 & 5 & -9 &k
\end{bmatrix}$$
Alright, we perform some steps:
1- We add 1 times row two to row three.
2- We multiply row one by 2.
3- We sum the row one and three.
But when we do step three, we get $2g+h+k=0$.It means that this equation should hold for the system to be consistent - I think my problem is just at the aforementioned step - However, I think when we get things like $0=0$ or $2=2$ , and these kind of equations which are true then we have infinite solutions.Am I right?
I have tested my answer and it doesn't work!
The real answer is $k-2g+h=0$, but why?
Thanks in advance