# Nonsingular math help

1. Feb 7, 2010

### Dustinsfl

1. The problem statement, all variables and given/known data
If A is nonsingular, then A can be factored into a product of elementary matrices.
True or False but justify the reason.

2. Relevant equations
The issue here is that in class we came to the conclusion false but the book says true. Can someone help me with the correct answer and reasoning? Thanks.

Last edited: Feb 7, 2010
2. Feb 7, 2010

### vela

Staff Emeritus
Re: Nonsingular

What was the reasoning your class used to conclude the statement was false?

3. Feb 7, 2010

### Dustinsfl

Re: Nonsingular

Because the multiplication of two elementary matrices equals the prodct of two elementary martices and the product may not be one step away from I.

4. Feb 7, 2010

### vela

Staff Emeritus
Re: Nonsingular

I don't follow how that leads to the conclusion that a non-singular matrix can't be written as a product of elementary matrices.

I think perhaps you're misinterpreting the statement. It's not saying that A=T1T2, where it's the product of only two elementary matrices. It will generally be the product of more than two elementary matrices.