Elementary Row Operations

• Oct 7th 2010, 01:38 PM
Ferny84
Elementary Row Operations
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?
• Oct 7th 2010, 02:04 PM
mr fantastic
Quote:

Originally Posted by Ferny84
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?

You can do operation #2 to as many rows as you want at the same time.
• Oct 8th 2010, 06:58 AM
HallsofIvy
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":
$\begin{bmatrix}3 & 4 \\ 1 & 2\end{bmatrix}\to \begin{bmatrix}3 & 4\\ 6 & 10\end{bmatrix}$
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.
• Oct 8th 2010, 12:50 PM
mr fantastic
Quote:

Originally Posted by HallsofIvy
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..

[snip]

Although you disagree, I suspect that you would agree with what I meant (perhaps I should have said you can do each one seperate but write down the result of them all as one augmented matrix ....)

(And no need to be fearful, I use my power on the guilty, not the innnocent).
• Oct 9th 2010, 03:44 AM
HallsofIvy
Yes, I agree with that.

(And I wasn't shaking with fear at the idea of you doing anything- just at the idea of disagreeing with such a great mind!)