Suppose that V is a vector space over R (not necessarily finite dimensional), and
that T1 : V −→ V and T2 : V −→ V are linear transformations from V to V with the
property that T3 = T2 ◦ T1 is the identity transformation, i.e. that T3(v) = v for all
vectors v in V.
T1(x1, x2, x3, . . .) = (0, x1, x2, x3, . . .)
T2(x1, x2, x3, x4, . . .) = (x2, x3, x4, . . .)
Check that T2 ◦ T1 is the identity transformation from V to V.

Question

Suppose that V is a vector space over R (not necessarily finite dimensional), and
that T1 : V −→ V and T2 : V −→ V are linear transformations from V to V with the
property that T3 = T2 ◦ T1 is the identity transformation, i.e. that T3(v) = v for all
vectors v in V.
T1(x1, x2, x3, . . .) = (0, x1, x2, x3, . . .)
T2(x1, x2, x3, x4, . . .) = (x2, x3, x4, . . .)
Check that T2 ◦ T1 is the identity transformation from V to V.

anonymous · Answer

i have a question... how do you ask a questiom?

anonymous · Answer

if you've asked a question already you have to close it so that you can ask another.

anonymous · Answer

reallly... aw man i miss the old open study, but i guess its for the better because people over post questions:)

turingtest · Answer

yep, that's why we changed it

amistre64 · Answer

it looks like most people are just closing their questions to post new ones; hoping that people browse thru the closed questions ....

anonymous · Answer

yea me tooo

amistre64 · Answer

what does t2.t1 mean in this context?

amistre64 · Answer

isnt t3(v) = v just a eugene type thing?

anonymous · Answer

i'm not sure, T1 and T2 are 2 transformations.

amistre64 · Answer

the open dot is whats a little confusing; does ot mean a dot product?  ie, multiplication

anonymous · Answer

i think its T2 of T1
Like .. T2(T1(x)))

amistre64 · Answer

hmm, never even heard of that in matrix stuff before

anonymous · Answer

maybe i'm wrong then

amistre64 · Answer

$$\begin{array}\ a_1x^1+a_2x^2+a_3x^3+a_4x^4+...+a_nx^n=0\
 b_1x^1+b_2x^2+b_3x^3+b_4x^4+...+b_nx^n=x\
 c_1x^1+c_2x^2+c_3x^3+c_4x^4+...+c_nx^n=x^2\
.\.\.\
 n_1x^1+n_2x^2+n_3x^3+n_4x^4+...+n_nx^n=x^{n+1}\
 \end{array}$$

im wondering if we would have to do an induction proof

amistre64 · Answer

might be easier with a different set of notations; using arxn and brxn for the coeefs

amistre64 · Answer

$$\begin{array}\
 a_{11}b_{11}+a_{12}b_{21}+...+a_{1n}b_{n1}=1& a_{11}b_{12}+a_{12}b_{22}+...+a_{1n}b_{n2}=0\
 a_{21}b_{11}+a_{22}b_{21}+...+a_{2n}b_{n1}=0& a_{21}b_{12}+a_{22}b_{22}+...+a_{2n}b_{n2}=1\
 a_{31}b_{11}+a_{32}b_{21}+...+a_{3n}b_{n1}=0& a_{31}b_{12}+a_{32}b_{22}+...+a_{3n}b_{n2}=0\
... &...\
 a_{n1}b_{11}+a_{n2}b_{21}+...+a_{nn}b_{n1}=0& a_{n1}b_{12}+a_{n2}b_{22}+...+a_{nn}b_{n2}=0\

\end{array}$$

then again, might be just as much of a pain

anonymous · Answer

maybe. ahh thanks anyways!