August 29th, 2011, 08:23 PM  #1 
Newbie Joined: Aug 2009 Posts: 29 Thanks: 0  Invertible matrix
Let A be an nxn matrix. Prove that if A is not invertible, then there exists an nxn matrix B such that but 
August 29th, 2011, 09:05 PM  #2  
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: Invertible matrix Quote:
If A is the zero matrix, then we are done. Otherwise, suppose that A is not the zero matrix, yet det(A) = 0. Then A has at least one nonzero entry, say A_ij = c, for some value of c, and some 0 <= i,j <= n ...  
August 29th, 2011, 09:24 PM  #3 
Newbie Joined: Aug 2009 Posts: 29 Thanks: 0  Re: Invertible matrix
The determinant of a matrix will be introduced after the section where this question is from. Aside from determinant, can we use any property of invertible matrix? Thanks for the help.

August 31st, 2011, 06:30 AM  #4 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: Invertible matrix
If an n by n maA is not "invertible", then it is not "onetoone". That is, there exist two distinct vectors, X and Y, such that AX= AY. Of course, AX AY= A(X Y)= 0.


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