Subjects linear algebra

Matrix Element Location

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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) $