I know that these are the elementary row operations:
Elementary Row Operations.
1. Interchange two rows. 2. Multiply a row with a nonzero number. 3. Add a row to another one multiplied by a number.
Are you allowed to multiply all rows by a non zero number at once or must it be done separately?
I disagree with mr fantastic on this (shaking with fear). An elementary row operation involves multiplying one row by a number. Of course you do as many row operations, one after the other, as you like- but not "at the same time" and call it an elementary row operation..
Oh, and "Add a row to another one multiplied by a number" is ambiguous. I would interpret it as, say, "multiply row 2 by
3 and add row 1 to it":
is NOT an elementary row operation (though it can be done by two consecutive row operations: multiply row 2 by 3 and then add row 1 to row 2.
"Add a multiple of one row to another row" is an elementary row operation.
(And no need to be fearful, I use my power on the guilty, not the innnocent).