Lets say I have a matrix: $$\left[\begin{array}{cc} 2 & 4 \\ 3 & 7 \\ \end{array}\right] $$
And my maximum range value is $10$, how would I go about creating another matrix that inverts those values? So that the matrix would end up looking like:
$$\left[\begin{array}{cc}
8 & 6 \\
7 & 3 \\
\end{array}\right]
$$
In algebraic form?
On
Look at the individual entries in the matrix, and see what relationship you can find between those entries, and the "maximum range value".
From your example, in the $(1,1)$ cell in the first matrix, you have the entry $2$. In the second matrix, you have the entry $8$. Your maximum value is $10$. Can you see some relationship between the numbers $2$, $8$, and $10$? Does this relationship hold for the other values? (for example, $3$, $7$, and $10$)
Leave a comment if you need more guidance. (I'm experimenting with my answering style from just giving an answer to trying a more Socratic method... so I'm looking for feedback.)
Based on your example, it looks like you're asking the following:
The answer to that question is: "Yes, but it isn't necessarily very interesting." Let $J$ be the $2\times 2$ matrix of $1$s. Then for any $m>0$ and any $2\times 2$ matrix $A$ with entries between $0$ and $m$ (inclusive), the matrix $m\cdot J-A$ does the trick (where $m\cdot J$ indicates scalar multiplication by $m$).
If that's not what you were trying to ask, then please clarify. It might help if you told us what led you to ask this question, too.