Matrix Element Location
1. **Problem statement:** Given the matrix
$$\begin{pmatrix}
6 & -5 & 1 & -3 \\
2 & -4 & 8 & 3 \\
4 & -7 & -6 & 5 \\
-2 & 9 & 7 & -1
\end{pmatrix}$$
find the position of the following elements using double suffix notation where the first index is the row and the second is the column, counting from the top-left as (1,1).
2. **Locate element 3:**
Look through each element starting from top-left.
- Row 1: Elements are 6, -5, 1, -3 → no 3 here.
- Row 2: Elements are 2, -4, 8, 3 → found 3 at the 4th column.
So, element 3 is at position $ (2,4) $.
3. **Locate element -1:**
- Row 4: Elements are -2, 9, 7, -1 → found -1 at the 4th column.
So, element -1 is at position $ (4,4) $.
4. **Locate element 8:**
- Row 2: Elements are 2, -4, 8, 3 → found 8 at the 3rd column.
So, element 8 is at position $ (2,3) $.
**Final answers:**
- Element 3: $ (2,4) $
- Element -1: $ (4,4) $
- Element 8: $ (2,3) $