Linear Transformation

  • Thread starter sana2476
  • Start date
  • #1
33
0

Homework Statement



Let V=<sinx,cosx> and T: V --> V be a transformation defined by T(f)=df/dx +f. Prove T is linear.



The Attempt at a Solution



T(f+g) = cosx-sinx+sinx+cosx
T(f)+T(g) = (sinx+cosx)'+sinx+cosx
= T(sinx)+T(cosx)

T(αf)=αcosx +αsinx
αT(f)= α(cosx+sinx)

Since we proved both addition and scalar, we can conclude that T is linear.
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,260
619
I think you are supposed to take f and g to be any linear combination of sin(x) and cos(x). I.e. f(x)=a*sin(x)+b*cos(x), g(x)=c*sin(x)+d*cos(x). So you've got the right idea, but you are only doing special cases.
 

Related Threads on Linear Transformation

  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
6
Views
1K
  • Last Post
Replies
1
Views
751
  • Last Post
Replies
4
Views
804
  • Last Post
Replies
6
Views
896
  • Last Post
Replies
7
Views
916
  • Last Post
Replies
9
Views
592
  • Last Post
Replies
10
Views
2K
Replies
4
Views
946
Replies
8
Views
1K
Top