I am not really sure where to even start with this problem. I am given a matrix with 1 missing value in the coefficient matrix. I am also told it is inconsistent, which as I understand means there are no solutions or a row could look like: $$\begin{array}{ccc} 0 & 0 &| 1\\ \end{array}$$ This is the matrix that I am given:
$$\begin{array}{ccc} 2 & h &| 4\\ 3 & 6 &| 7\\ \end{array}$$
I tried to reduce the matrix first by:
$$R2 \leftarrow R1(-3) + R2(2)$$ $$\begin{array}{ccc} 2 & h &| 4\\ 0 & 12-3h &| 2\\ \end{array}$$
Not sure if I am on the right track or not, but I just don't know where to go from here.
I know that there are similar questions to this one on this forum, but I just don't understand the solutions, and the question matrices are a bit more complicated. So, I apologize up front for the repeat, I just need an "Explain to me like I'm 5".
Thank you for a quick response, and not just answering my problem for me. For those of you reading this with a similar question. First thank you to Anurag A!
If this is not the proper answer please feel free to correct it or let me know how I went wrong.
After reducing the augmented matrix we have: $$R2 = 0x + (12-3h)y = 2$$
In order to solve we must find where $12-3h=0$ meaning $h=4$
or $$\begin{array}{ccc} 2 & 4 &| 4\\ 3 & 6 &| 7\\ \end{array}$$
Hopefully, that is right!