Question

Linear algebra: Subspaces (general)
http://prntscr.com/aku7l8
(the answers I have are correct)
I'm not sure I understand this P(0) business and how it relates to the zero vector - what's going on?

Answer 1

like what does P(0) do in the context of this problem? does it guarantee existence of a zero vector or something?

Answer 2

Yeah, you have to check whether it's a subspace so if you remember from last time, the closure of addition/ scalar mult/ 0 vector, the p(0)=0 implies it has the 0 polynomial.

So for example lets say we have a W={3+bx+cx^3} p(0)=3 for P_2 (second degree polynomial) this would not be a subspace of P_2 since it does not contain the zero polynomial which is p(0)=0.

Not sure if this is what you were looking for, but hope it helps.

Answer 3

ohhh okay thank you

Answer 4

Np