Sometimes, if you want students to manipulate some sort of special matrices (like, asking if they are invertible or ask for a LU decomposition, etc.), you have to possibility to state all properties of that special matrix in a rigorous way. Moreover, since it is a matrix, you can additionally show a picture of that matrix with a lot of $\ldots$ in it.
The problem, however, is that for some students the picture is helpful; for other students, it is distracting or misleading.
An example question:
Let $A$ be a tridiagonal matrix (i.e., $a_{ij}=0$ for $j>i+1$ and for $i>j+1$) with an non zero element $a_{n1}\neq 0$, i.e., the matrix looks like $$A = \begin{pmatrix} * & * & 0 & \ldots & \ldots & 0 \\ * & \ddots & \ddots & \ddots & & \vdots \\ 0 & \ddots & \ddots & \ddots & \ddots & \vdots \\ \vdots & \ddots & \ddots & \ddots & \ddots & 0 \\ 0 & & \ddots & \ddots & \ddots & * \\ * & 0 & \ldots & 0 & * & * \end{pmatrix}$$ where $*$ means that on this location, there is an arbitrary real number which can be different from zero. Let $LU=A$ be a LU-decomposition of $A$. Perform an LU decomposition of $A$ in order to find the locations in $L$ and $U$ which are zero for sure.
Several students manipulated the matrix and arrived at some point to calculate things like $$\frac{*}{*}=1, \quad *-*=0$$ etc. which is not true since the interpret $*$ as a fixed number.
How can one avoid such misinterpretations of the picture? What went wrong when students perform calculations like above? Should one avoid pictures like the above? Should one write even more text to make sure the meaning of $*$?