- #1
endfx
- 10
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I'm really confused about a question I came across in my textbook.
It basically says this:
Consider the set of polynomial functions of degree 2. Prove that this set is not closed under addition or scalar multiplication (and therefore not a vectorspace).
I'm confused because I think it is closed under addition and scalar mult.
example:
f(x) = ax^2 + bx + c
g(x) = dx^2 + ex + f
(f+g)(x) = (a+d)x^2 + (b+e)x + (c+f)
(sf)(x) = (sa)x^2 + (sb)x + sc
both results should be in the set of polynomial functions of degree 2.
Why would the question say it is not closed under addition and scalar mult. ??
Am I missing something very basic here, or could it be a trick question or something?
Thanks!
It basically says this:
Consider the set of polynomial functions of degree 2. Prove that this set is not closed under addition or scalar multiplication (and therefore not a vectorspace).
I'm confused because I think it is closed under addition and scalar mult.
example:
f(x) = ax^2 + bx + c
g(x) = dx^2 + ex + f
(f+g)(x) = (a+d)x^2 + (b+e)x + (c+f)
(sf)(x) = (sa)x^2 + (sb)x + sc
both results should be in the set of polynomial functions of degree 2.
Why would the question say it is not closed under addition and scalar mult. ??
Am I missing something very basic here, or could it be a trick question or something?
Thanks!