My Math Forum  

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

Linear Algebra Linear Algebra Math Forum

LinkBack Thread Tools Display Modes
April 25th, 2015, 01:05 AM   #1
Joined: Apr 2015
From: HK

Posts: 2
Thanks: 0

3 questions about matrix

I have already try my best to do it, but still can't solve it
Thank you for everyone who try to answer my question!

mannok is offline  
April 25th, 2015, 03:46 AM   #2
Math Team
Joined: Jan 2015
From: Alabama

Posts: 3,264
Thanks: 902

These all pretty straightforward problems. If you really cannot do them, you must be missing something basic.

For the first, to say that v is an eigenvector of A with eigenvalue -7 means that Av= -7v. So A^2v= A(Av)= -7Av= -7(-7v)= (-7)^2v= 49v. Then A^3v= A(A^2v)= 49Av= 49(-7v)= (-7)^3v, etc

Since Av= -7v, A^-1(Av)= v= -7A^-1v so that A^-1v= (-1/7)v.

(A- 5I)v= Av- 5Iv= -7v- 5v= -12v

For the second, if a matrix, A, is "diagonalizable", then there exist matrix P such that A= PDP^-1 where D is a diagonal matrix having the eigenvalues of A on its diagonal and P has the corresponding eigenvectors of A as its columns.

The simplest way to find a high power of a (diagonalizable) matrix is to first diagonalize it. If A= PDP^-1, then A^n= PD^nP^-1.
Country Boy is offline  

  My Math Forum > College Math Forum > Linear Algebra

matrix, questions

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
ultra diagonal matrix, super diagonal matrix, sub diagonal matrix silviatodorof Linear Algebra 2 March 22nd, 2015 05:28 AM
Need solutions for these matrix questions omer1994 Linear Algebra 1 August 10th, 2014 02:37 PM
Matrix Questions imirish85 Linear Algebra 0 March 4th, 2011 10:22 AM
questions on matrix diagonalization excellents Linear Algebra 0 October 17th, 2009 08:12 AM

Copyright © 2019 My Math Forum. All rights reserved.