My Math Forum  

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

Linear Algebra Linear Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
March 24th, 2010, 08:11 PM   #1
Senior Member
 
Joined: Sep 2009

Posts: 115
Thanks: 0

Representation Question

(note when I say a0 or a1 I mean alpha subscript 0 or alpha subscript 1: and when I say t i mean the math symbol that looks like a t (I think it's called tao)
define the mapping T from R4[t] to R4[t] by:
T(a0 + a1*t + a2*t^2 + a3*t^3)=a0 + a1*t + a2((1.5*t^2)-0.5) + a3((2.5*t^3)-1.5*t)
Let X=(1 , t , t^2 , t^3)
1.find A=RxxT.
2.show that A (and hence T) is nonsingular.
3. Find bases V and W such that RwxT and RxvT are each the identity matrix.
I am stuck, I tried doing number 1 but I am not sure if I am right: I got
a0 0 0 0
0 a1 0 0
a= -0.5*a2 0 1.5*a2 0
0 -1.5*a3 0 2.5*a3

(this being the matrix)

and I am not sure about the rest.
Thank you in advance.
wannabe1 is offline  
 
Reply

  My Math Forum > College Math Forum > Linear Algebra

Tags
question, representation



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
representation of permutation bvh Advanced Statistics 1 February 28th, 2013 08:47 AM
Matrix Representation playthious Linear Algebra 1 March 22nd, 2012 01:26 PM
Integers representation loes Number Theory 1 April 16th, 2010 12:19 PM
Representation of sets klendo Applied Math 6 December 16th, 2009 02:14 AM
Question on a Basis Representation question Hellfire1987 Number Theory 3 November 23rd, 2009 02:15 PM





Copyright © 2018 My Math Forum. All rights reserved.