Register to reply 
Prove that a matrix A is invertible if and only if its reduced row echelon row is the 
Share this thread: 
#1
Jun3008, 09:01 PM

P: 25

Prove that a matrix A is invertible if and only if its reduced row echelon row is the identity matrix.



#2
Jun3008, 09:30 PM

HW Helper
P: 6,202

Even though I was never taught linear algebra fully, to do this problem I would consider what would make the matrix A invertible and what would it mean if the RRE form wasn't the identity matrix.
But I am not sure if that would be a valid proof. 


#3
Jul108, 12:08 AM

HW Helper
P: 2,616

This isn't too hard to prove. You can start by asking yourself what a row operation on a matrix translates to in matrix algebra. And what do the matrices corresponding to the rowoperations amount to when they rowreduce A to I?
As for the "forward" conjecture, well I can think of something some might find objectionable. If it does not rowreduce A to I, it the RRE form has a row of zeros. That means that the determinant is 0 and hence it is not invertible. I'm sure there's a better way to do this. 


Register to reply 
Related Discussions  
Two square invertible matrices, prove product is invertible  Calculus & Beyond Homework  1  
RowReduced Echelon Forms  Linear & Abstract Algebra  7  
Determinant of a matrix using reduced echelon form  Precalculus Mathematics Homework  7  
Reduced row echelon form of matrix  Linear & Abstract Algebra  1  
Reduced row echelon form  Introductory Physics Homework  1 