Skill: Identify a matrix element from its row and column indices

In the notation $a_{ij}$, the first index $i$ tells you the row, and the second index $j$ tells you the column. Find the row first, then move across to the column.

For example, let

$$A=\begin{bmatrix} 4&-1&7&2\\ 0&5&3&-6\\ 8&9&1&4 \end{bmatrix}.$$

Find $a_{23}$.

1. The first index is $2$, so look at row 2: $[0,\ 5,\ 3,\ -6]$.
2. The second index is $3$, so select the third entry in that row.

Therefore, $a_{23}=3$. The matrix has 3 rows and 4 columns, so both indices are within its dimensions. Remember: reversing the indices would mean a different row and column.