- #1
discoverer02
- 138
- 1
I'd like to check my proof. It seems easy enough, but I'd like to make sure that I'm not missing anything:
If V is the space of all continuous functions on [0,1] and if
Tf = integral of f(x) from 0 to 1 for f in V, show that T is a linear transformation From V into R1.
Like I said the proof seems simple enough, but I just want to make sure I'm not missing anything that might be implied by "From V into R1."
T(f + g) = integral from 0 to 1[f(x) + g(x)]dx
= integral from 0 to 1 f(x)dx + integral from 0 to 1 g(x)dx
= Tf + Tg
T(kf) = integral from 0 to 1 kf(x)dx
= k*integral from 0 to1 f(x)dx
= kTf
there for T is a linear transformation.
I feel silly posting something this simple, but I'm just not absolutely sure that I'm not missing something.
Thanks as usual for all the help.
If V is the space of all continuous functions on [0,1] and if
Tf = integral of f(x) from 0 to 1 for f in V, show that T is a linear transformation From V into R1.
Like I said the proof seems simple enough, but I just want to make sure I'm not missing anything that might be implied by "From V into R1."
T(f + g) = integral from 0 to 1[f(x) + g(x)]dx
= integral from 0 to 1 f(x)dx + integral from 0 to 1 g(x)dx
= Tf + Tg
T(kf) = integral from 0 to 1 kf(x)dx
= k*integral from 0 to1 f(x)dx
= kTf
there for T is a linear transformation.
I feel silly posting something this simple, but I'm just not absolutely sure that I'm not missing something.
Thanks as usual for all the help.