In the discussion, it is established that any set of more than three vectors in the polynomial space P2 is linearly dependent. The example provided includes the set S = {1, x, x^2}, which is confirmed to be linearly dependent as it can be represented by the zero vector (a_0, a_1, a_2) = (0, 0, 0). The Wronskian is mentioned as a tool for proving linear independence but is clarified that it does not demonstrate linear dependence. The confusion surrounding the application of the Wronskian on the set {1, x, x^2, x^3} is also addressed.
PREREQUISITESThis discussion is beneficial for students and educators in linear algebra, mathematicians exploring polynomial spaces, and anyone interested in the concepts of linear dependence and independence in vector analysis.
delgeezee said:i know S = { $$1 , x, x^2$$} is linearly dependent set for p2. where $$(a_0, a_1, a_2) = (0,0,0) $$
I wanted to use the Wronskian on { $$1 , x, x^2, x^3$$} , but as I understand, it only proves linear independence and not the converse.