Practice question · Sort into groups
Sort each manipulation by whether it is a legitimate row operation on a system.
Groups: Valid row operation · Not a valid row operation
- Add 2 times row 1 to row 3
- Add one column to another column
- Multiply a row by 3
- Swap two rows
- Replace row 2 by row 2 minus row 1
- Multiply a row by 0
Hints
- The test is whether the operation can be undone, so that the solution set is preserved.
- Multiplying by 0 destroys an equation, and columns are variables, not equations.
Show the answer
Valid row operation: Swap two rows, Multiply a row by 3, Add 2 times row 1 to row 3, Replace row 2 by row 2 minus row 1
Not a valid row operation: Multiply a row by 0, Add one column to another column
Why
The three legal operations are swap, scale by a NONZERO number, and add a multiple of one row to another. Scaling by 0 wipes out an equation and cannot be reversed, so it can create solutions that were not there. Column operations mix up the variables themselves and are not row operations at all.
Practise Systems of Linear Equations
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