Worked through Axler exercises in section 3.F, 28-31.
Some general feeling of missing important results about null T', nothing when I reviewed chapter
Approached this by trying to prove there is a basis of V these lin ind functionals are dual of (turned out to be problem 31), the proof was a combination of commerelial and entational symbolic manipulation to build up the construction.
List of vectors to "fill" the rest of the dimension ejudes out to the right.
Snippet of construction: "ϕ3 must be non-zero for one of these" accompanied by entational list of v3-vn.
Seems like conversational commerel + entational manipulation + looking for some feeling of "confirmation" (or lack of disconfirmation?).