2 4 6 8
-1 2 4 3
4 -4 0 0
-2 1 0 0
0 0 0 0 piviot the system about the element in row 2 colum 1 enter the augmented matrix with the cell in their original position
To pivot the system about the element in row 2 column 1, we need to perform elementary row operations to make all elements except the pivot element become zero.
1. First, we initialize the pivot element as the value in row 2 column 1, which is -2.
2. To create zeros in the first column below the pivot element, we perform the following operations:
a) Replace row 1 by (row 1) + (-1) * (row 2) to make the first element in row 1 zero.
The new row 1 will be: (2, 4, 6, 8) + (-1) * (-2, 1, 0, 0) = (2, 4, 6, 8) + (2, -1, 0, 0) = (4, 3, 6, 8).
b) Replace row 3 by (row 3) + 0 * (row 2) since the element in row 3 column 1 is already zero.
The new row 3 remains the same: (0, 0, 0, 0).
3. The pivoted augmented matrix with the cells in their original positions after performing the row operations is:
4 -4 0 0
4 3 6 8
0 0 0 0