Linear Algebra question
Favorites|Homepage
Subscriptions | sitemap
HOME > > Linear Algebra question

Linear Algebra question

[From: ] [author: ] [Date: 11-12-31] [Hit: ]
each of which is invertible.So,R = E_k * E_(k-1) * ...Where each E_i is an elementary matrix.......
A is an mxn matrix with reduced row echelon form R.Prove that if rank A
-
The proof comes from the definition of reduced-row-echelon form. In order to get from the original form (A) to the reduced form (R), we multiply the matrix A by "elementary matrices," each of which is invertible. So, we have the following equality:

R = E_k * E_(k-1) * ... * E_3 * E_2 * E_1 * A

Where each E_i is an elementary matrix. We can rewrite this as

R = P * A

where P is the product of these Elementary matrices. If rank(A)
F*R = P*A

since F is invertible, we can write

R = F^-1 * P * A

Thus, (F^-1 * P) and P are two different invertible matrices that work.

QED

-
i actually dont know
1
keywords: Linear,Algebra,question,Linear Algebra question
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .