Creating a 5x5 Matrix with a Specific Pattern

To create the given 5x5 matrix, we can start by writing the pattern that we observe:

$$\begin{array}{|c|c|c|c|c|}\hline\0 & 1 & 0 & 0 & 0\hline\1 & 0 & 1 & 0 & 0\hline\0 & 1 & 0 & 1 & 0\hline\0 & 0 & 1 & 0 & 1\hline\0 & 0 & 0 & 1 & 0\hline\end{array}$$

From this pattern, we can see that the diagonal entries are all 0, and the off-diagonal entries are 1. Therefore, the matrix can be defined as:

$$\begin{bmatrix}\0 & 1 & 0 & 0 & 0\1 & 0 & 1 & 0 & 0\0 & 1 & 0 & 1 & 0\0 & 0 & 1 & 0 & 1\0 & 0 & 0 & 1 & 0\end{bmatrix}$