Pivot the system about the element in row 2, column 1.
[3 3| –2]
[–9 –4| 1]
To pivot the system about the element in row 2, column 1, you need to make that element the pivot element. The pivot element should be a non-zero number.
In this case, the element in row 2, column 1 is -9. Since it is already non-zero, we can proceed to pivot the system.
To pivot the system, we need to perform row operations to make all other elements in the column except the pivot element equal to zero. The goal is to create a column with only one non-zero element, which will be the pivot element.
Let's perform the row operations step by step:
1. Divide row 2 by -9 to make the pivot element equal to 1:
[3 3| –2]
[(1/(-9)) (-4/(-9))| (1/(-9))]
Simplifying row 2:
[3 3| –2]
[-1/9 4/9| -1/9]
2. Multiply row 2 by 3 and add it to row 1 to eliminate the element in row 1, column 1:
[3+(-1/9)*3 3+(-1/9)*3| –2+(-1/9)*(-2)]
[0 (3/9)-(4/9)*3| (2/9)-(-1/9)*(-2)]
Simplifying row 1:
[0 (3/9)-(4/9)*3| (2/9)-(-1/9)*(-2)]
[0 -1 (2/9)-(-1/9)*(-2)]
Simplifying row 2:
[-1/3 0| 1/3]
Now, the system is pivoted about the element in row 2, column 1. The pivot element is 1, and all other elements in the column are zero, except for the pivot element.