Practice question · Put in order
Order the steps of solving a system by Gaussian elimination with partial pivoting.
- Move to the next column and repeat
- Arrive at an upper-triangular system
- In the current column, find the largest entry and swap its row into the pivot position
- Back-substitute from the last equation upward
- Eliminate the entries below the pivot
Hints
- The swap happens before the elimination that will divide by the pivot.
- Back-substitution needs a triangular system to work on.
Show the answer
- In the current column, find the largest entry and swap its row into the pivot position
- Eliminate the entries below the pivot
- Move to the next column and repeat
- Arrive at an upper-triangular system
- Back-substitute from the last equation upward
Why
Pivot selection must precede elimination, since it exists to make the division safe. Only once the whole matrix is triangular can back-substitution begin, the two phases are strictly sequential.
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