How would I do this question.
Determine the value(s) of $h$ such that the matrix is augmented of a consistent linear system.
My matrix \begin{bmatrix} 1&h&4\\ 3&6&8 \end{bmatrix}
I am not sure how to format it very well in latex. But I do not get this question I am not sure what they are asking. I just know how to find x and y.
On
Since this matrix represents a system in x and y, once the answer given by row-reducing the matrix, it might be useful to a better understanding to graph the straight lines x+hy=4 and 3x+6y=8 for a few values of h, of course using the value h=2 and some other near h=2. For example h=2.1 or h=1.75 and also for h=1 and h=3.
To determine if an augmented matrix represents a consistent linear system, you row-reduce it to find the solution set; I assume you know this. So row-reduce this matrix. The system is consistent if there is no row of the form $0\ 0\ x$ where $x\ne 0$. You should be able to find conditions on $h$ which guarantee that this will not happen.