# Determine the values(s) of h and/or k such that the matrix is the augmented matrix of a consistent system.

\begin{bmatrix} 2 && -1 && 3 && h \\ 1 && 0 && 4 && k \\ -6 && 3 && -9 && 15 \end{bmatrix}

Ok let me give some background. I believe I have dyscalculia, so when the teacher never specifically went over these specific kinds of problems it left me paranoid. Math to me has to be understood visually and in proof terms. I need help understanding the specific steps to this problem and why those steps are required. It would help if you do not assume anything about what I may or may not understand and explain everything thoroughly. Or at least link somewhere that explains it well. I have been researching problems similar and all the explanations do not break it down well enough for me. I was going o ignore these kinds of problems, but I really want to understand them.

So far in class I am able to solve systems of equations in augmented matrices just fine. What confuses me is adding random variables to the mix. So I understand basic row equations and for the most part understand why certain row equations are made to get into reduced row echelon form. This one just has left me stumped. So can someone please help me.

Side Note: I often use a white board and marker to visualize math concepts + mix Khan Academy and other online resources to strengthen my mathematical understanding.If any of you are willing, please let me know if I can get some 1 on 1 math help with someone. I really want to conquer math, even though everything is against me.

• Are you familiar with Gauss elimination? – imranfat Sep 6 '16 at 15:44
• hello thank you so much for the response, I think I am. I am looking at this link currently, Inline Link, could you explain how I use this to solve this problem? It is hard doing it without any similar examples. – EpistemicPolymath Sep 6 '16 at 16:18
• First step, interchange rows 1 and 2, why is that? – imranfat Sep 6 '16 at 17:14
• From my understanding, you would take that step so that you already have a "pivot" on the first row? Is that right? – EpistemicPolymath Sep 6 '16 at 17:23
• Yes, now you can perform a subtraction: Row 2 minus 2 times Row 1 to form a new row 2. That would be the next step. For the new third row: Add 6 times row 1 to it. – imranfat Sep 6 '16 at 17:26