Is A Nonsingular? True or False: Elementary Matrix Factorization Explained

[Dustinsfl]

Homework Statement

If A is nonsingular, then A can be factored into a product of elementary matrices.
True or False but justify the reason.

Homework 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.

 

[vela]

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

 

[Dustinsfl]

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.

 

[vela]

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.