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Show that in every set p2 with more than three vectors is linearly dependent.

delgeezee

New member
May 24, 2013
9
i know S = { \(\displaystyle 1 , x, x^2\)} is linearly dependent set for p2. where \(\displaystyle (a_0, a_1, a_2) = (0,0,0) \)
I wanted to use the Wronskian on { \(\displaystyle 1 , x, x^2, x^3\)} , but as I understand, it only proves linear independence and not the converse.
 

Klaas van Aarsen

MHB Seeker
Staff member
Mar 5, 2012
8,894
i know S = { \(\displaystyle 1 , x, x^2\)} is linearly dependent set for p2. where \(\displaystyle (a_0, a_1, a_2) = (0,0,0) \)
I wanted to use the Wronskian on { \(\displaystyle 1 , x, x^2, x^3\)} , but as I understand, it only proves linear independence and not the converse.
Hi delgeezee!

Can you elaborate?
For starters, what do you mean by p2?
And how do your $a_i$ tie in?