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#1 2017-03-12 21:45:40

Registered: 2014-04-15
Posts: 44

Matrix inverse proof

Let A be a n*n matrix and

Hi, I'm having trouble with the above question. I've made a start but I'm not sure if I'm approaching it correctly.
First of, there's a hint that suggests that I first consider the product AX. But if I do that, the dimensions of A and X are different so I would need to find the transpose of X?
so is it safe to assume


To find if A is invertible can I also do the following?
AX=XB (where B is some solution of A)

and for the formula:


#2 2017-03-14 02:53:20

From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Matrix inverse proof


First and second line.

Shelled wrote:

(where B is some solution of A)

A is an n x n matrix and B is n x 1 column vector... so how can they be equal?

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.


#3 2017-12-25 01:57:29

Registered: 2006-03-12
Posts: 1,332

Re: Matrix inverse proof

AX =  X diag( 入i )

V := X^(-1)

AX diag( 1/ 入i )V  =  X diag( 入i )diag( 1/ 入i ) V  = I


A^(-1) =  X diag( 1/ 入i ) X^(-1)



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