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nautolian
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1. Let V={(X^2+X+1)p(x) : p(x) [itex]\in[/itex] P2(x)}
Show that V is a subspace of P4(x). Display a basis, with a proof. What is the dimension of V?
2.
3. I started to try to figure out how to prove that V is a subspace of P4, but I'm not sure how.
To show that it is closed under addition:
p(x)=x^2 is in P2(x)
(x^2+x+1)(x^2)+(a^2+a+1)(a^2)
x^4+x^3+x^2+a^4+a^3+a^2 is in P4, because no exponent is greater than 4.
The zero vector is if p(x) = 0
And then I'm not sure how to show that multiplication is closed
Show that V is a subspace of P4(x). Display a basis, with a proof. What is the dimension of V?
2.
3. I started to try to figure out how to prove that V is a subspace of P4, but I'm not sure how.
To show that it is closed under addition:
p(x)=x^2 is in P2(x)
(x^2+x+1)(x^2)+(a^2+a+1)(a^2)
x^4+x^3+x^2+a^4+a^3+a^2 is in P4, because no exponent is greater than 4.
The zero vector is if p(x) = 0
And then I'm not sure how to show that multiplication is closed
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