My Math Forum  

Go Back   My Math Forum > College Math Forum > Linear Algebra

Linear Algebra Linear Algebra Math Forum

LinkBack Thread Tools Display Modes
November 27th, 2009, 02:39 PM   #1
Senior Member
Joined: Nov 2009

Posts: 169
Thanks: 0

Show that A must be invertible

Let be a polynomial of degree n in x with real coefficients. For any mxm matrix A, we define .
Show that, if and , then A must be invertible. [Hint: isolate Im from the equation P(A) = 0m]

For A =
[2 2 -1]
[-1 -1 1]
[2 4 -1] , compute , if , calculate P(A). ) Can you explan this,>?

For p(A), How can I subtract 2 from a mtrix?
450081592 is offline  
November 28th, 2009, 01:32 AM   #2
Senior Member
Joined: Oct 2007
From: Chicago

Posts: 1,701
Thanks: 3

Re: Show that A must be invertible

Subtracting 2 from a matrix is really subtracting 2I... that is

P(A) (as a formula on matrices) will be A^2 + A - 2I

Does that answer your question or is there something I missed?

Also, in latex, you can get subscripts as well; just but _ after the letter. E.g. a_0 gives you
If you need more than one symbol in the subscript, wrap it in brackets. So A_{0,0} gives you
cknapp is offline  

  My Math Forum > College Math Forum > Linear Algebra

invertible, show

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Invertible Functions ceity Calculus 2 January 20th, 2014 02:08 AM
Why Isn't This Matrix Invertible? Magnesium Linear Algebra 2 December 11th, 2013 02:09 AM
With characteristic polynomial show that A is invertible skrat Linear Algebra 2 May 17th, 2013 04:04 AM
invertible matrix shine123 Linear Algebra 1 September 21st, 2012 08:47 AM
T: V to V and [T]_B is invertible tinynerdi Linear Algebra 0 February 20th, 2010 05:58 PM

Copyright © 2019 My Math Forum. All rights reserved.