- #1
amolv06
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Homework Statement
Determine whether the following is a subspace of [tex]P_{4}_[/tex]
(a) The set of polynomials in [tex]P_{4}[/tex] of even degree.
Homework Equations
[tex]P_{4} = ax^{3}+bx^{2}+cx+d[/tex]
The Attempt at a Solution
[tex](p+q(x)) = p(x) + q(x)[/tex]
[tex](\alpha p)(x) = p(\alpha x)[/tex]
If p and q are both of degree 2 then both scalar multiplication and vector addition should return a polynomial of degree 2 as far as I can tell, however my book states that this is not a subspace of [tex]P_{4}[/tex]. I can't tell why it wouldn't be.