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daniel_i_l
Gold Member
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Homework Statement
Let:
[tex] \alpha \in C_{4}[x] [/tex] (the space of all 4-deg complex ploymonials)
We'll define:
[tex]
U = Sp( \{\ x^3 - 2i \alpha x, x^2 +1 \} ) \\
W = Sp( \{\ x^3 + ix, (1-i)x^2 - \alpha x \})
[/tex]
as subspaces of [tex]C_{4}[x] [/tex]
a) find all values of alpha so that:
[tex] W \cap U \neq \{ 0 \} [/tex]
b) does:
[tex] C_{4}[x] = W \oplus U [/tex]
when alpha = 0?
Homework Equations
If [tex] C_{4}[x] = W+U [/tex] and [tex] W \cap U = {0} [/tex]
then [tex] C_{4}[x] = W \oplus U [/tex]
The Attempt at a Solution
I'm not sure how to approch this question. Do I find all the cases where
[tex] W \cap U = {0} [/tex] and then write the answer as all the other cases? To do that do I first find all the alphas where u = w for some u in U and for some w in W and then check which one of those forces both u and w to be 0?
And for b, if the answer in a isn't 0 then the answer is no right?
Thanks.
EDIT: Where did all the curly brackets go?
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