Practice question · Sort into groups
Which moves are legal row operations in Gaussian elimination?
Groups: Legal row operation · Illegal move
- Delete an inconvenient equation
- Square both sides of one equation
- Multiply a row by 5
- Add twice row 1 to row 2
- Multiply a row by 0
- Swap row 1 and row 3
Hints
- A legal operation must be reversible.
- Anything that destroys information or changes the solution set is out.
Show the answer
Legal row operation: Swap row 1 and row 3, Multiply a row by 5, Add twice row 1 to row 2
Illegal move: Multiply a row by 0, Delete an inconvenient equation, Square both sides of one equation
Why
Legal operations are reversible, they preserve the solution set exactly. Multiplying by zero erases information; deleting or squaring changes what the system says.
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