• Support PF! Buy your school textbooks, materials and every day products Here!

Linear transformations

  • Thread starter baddin
  • Start date
  • #1
24
0
1. Give information
Let T: P3 ---> P3 be the linear transformation described by:
T(p(x))=p(x+1)+p(2-x).
Find the matrix of T with respect to the standard basis b {1,x,x^2,x^3}.


The Attempt at a Solution


I found the transformations on the standard basis b:
T(1) = 2
T(x) = 3
T(x^2) = 2x^2 -2x +5
T(x^3) = 9x^2 - 9x + 9
I am confused on what to do next...
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
1. Give information
Let T: P3 ---> P3 be the linear transformation described by:
T(p(x))=p(x+1)+p(2-x).
Find the matrix of T with respect to the standard basis b {1,x,x^2,x^3}.


The Attempt at a Solution


I found the transformations on the standard basis b:
T(1) = 2
T(x) = 3
T(x^2) = 2x^2 -2x +5
T(x^3) = 9x^2 - 9x + 9
I am confused on what to do next...
Write your functions so they look a little more like vectors, write a+bx+cx^2+dx^3 as the column vector [a,b,c,d]. So T(1)=2 becomes T([1,0,0,0])=[2,0,0,0]. Does that help?
 
  • #3
24
0
Ok, then I should find T(1,0,0,0), T(0,1,0,0), T(0,0,1,0) and T(0,0,0,1) right?
 
  • #4
Dick
Science Advisor
Homework Helper
26,258
618
Ok, then I should find T(1,0,0,0), T(0,1,0,0), T(0,0,1,0) and T(0,0,0,1) right?
Right. You really already did. Just write them as column vectors. Then those will be the columns of your matrix.
 
  • Like
Likes 1 person
  • #5
24
0
Okay thank you very much for your help =)
 

Related Threads on Linear transformations

  • Last Post
Replies
4
Views
769
  • Last Post
Replies
1
Views
710
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
7
Views
879
  • Last Post
Replies
6
Views
862
  • Last Post
Replies
9
Views
567
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
8
Views
2K
Replies
8
Views
1K
Replies
4
Views
913
Top