Thread: 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....

Please give your new threads different titles if you start a number at once.

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

RonL

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