# Algebra3

• May 11th 2006, 06:29 PM
suedenation
Algebra3
In the Gauss-Jordan algorithm, the three elementary row operations that may be performed on an n x m matrix are:
(i) Interchange two rows
(ii) Multiply a row by a nonzero constant
(iii) Add a multiple of one row to another row
Are these threeoperations independent, or can one of them be performed using ony the other two operations?

Thanks very much.... :)
• May 11th 2006, 11:46 PM
CaptainBlack

It would be nice to be able to tell which is which

RonL
• May 11th 2006, 11:52 PM
CaptainBlack
Quote:

Originally Posted by suedenation
In the Gauss-Jordan algorithm, the three elementary row operations that may be performed on an n x m matrix are:
(i) Interchange two rows
(ii) Multiply a row by a nonzero constant
(iii) Add a multiple of one row to another row
Are these threeoperations independent, or can one of them be performed using ony the other two operations?

Thanks very much.... :)

To show that they are independent you need to show that:

1. Using just ii and iii you cannot achive i, for at least one matrix
2. Using just i and iii you cannot achive ii, for at least one matrix
3. Using just i and ii you cannot achive iii, for at least one matrix

Use the 2x2 or 3x3 identity matrix as your example matrix.

RonL