Can Rows be Combined Without Type III Operations?

[CuppoJava]

Homework Statement

Show that any multiple of a row can be added to a row above it by row operations of other types.

Homework Equations

There are only 3 elementary row operations.
i. Interchange two rows
ii. Multiply a row by a constant
iii. Add a multiple of a row to another row.

The Attempt at a Solution

I don't think it is possible and would like to confirm this. Without using type iii operations, there is no method of combining two rows.

Thanks for your help
-Patrick

 

[Dick]

You mean can i) and ii) be combined to show iii)? Doesn't seem likely, does it?

 

[CuppoJava]

No it seems quite impossible. I'm glad my mathematical intuition isn't completely failing me yet. Thanks Dick!
-Patrick