Pivot the system about the element in row 2, column 1.
–5 5 –7
10 4 4
To pivot a system about a specific element, we need to perform row operations that will eventually make the desired element the pivot element. Here's how to pivot the given system about the element in row 2, column 1:
Step 1: Start with the given system:
-5 5 -7
10 4 4
Step 2: Swap row 1 with row 2 to make the desired element the pivot element:
10 4 4
-5 5 -7
Step 3: Perform row operations to make the elements below the pivot zero:
Multiply row 1 by 0.5 and add it to row 2:
10 4 4
0 7 -5
Step 4: The system is now pivoted about the element in row 2, column 1:
10 4 4
0 7 -5
Now the element in row 2, column 1 is the pivot element.