U∩W

[TheWrathOfMath]

A agree withe dimension part, but have you tried to verify the result. I.e., does it satisfy both criteria, i.e., for U and W?

Yes.
I took 2cx+cx^2+2ex^3+ex^4 and substituted in the condition of U, so that:

2c(-1)+c(-1)^2+2e(-1)^3+e(-1)^4 =0
.
.
.
e=-c, therefore:

2cx+cx^2-2cx^3-cx^4
c(2x+x^2-x^3-x^4), hence the basis for the intersection is {2x+x^2-x^3-x^4}.

 

[blamocur]

If [imath]q(x) = 2x + x^2 - x^3 - x^4[/imath] then what is [imath]q(-1)[/imath]?

 

[TheWrathOfMath]

If [imath]q(x) = 2x + x^2 - x^3 - x^4[/imath] then what is [imath]q(-1)[/imath]?

q(-1)= -1

 

[blamocur]

q(-1)= -1

Don't you need 0 there? I.e., if [imath]q\in U \cap W[/imath] shoudn't it satisify criteria for both U and W?

 

[TheWrathOfMath]

Don't you need 0 there? I.e., if [imath]q\in U \cap W[/imath] shoudn't it satisify criteria for both U and W?

I am afraid that I do not understand your question.

 

[blamocur]

I am afraid that I do not understand your question.

I wanted you to verify your answer by using the fact that [imath]q \in U[/imath] means that [imath]q(-1) = 0[/imath].

 

[TheWrathOfMath]

I wanted you to verify your answer by using the fact that [imath]q \in U[/imath] means that [imath]q(-1) = 0[/imath].

I see. Perhaps my explanation was faulty, but what I did is correct, right?
I believe that I got the correct basis for the intersection.

 

[blamocur]

I see. Perhaps my explanation was faulty, but what I did is correct, right?
I believe that I got the correct basis for the intersection.

How can your answer for [imath]q[/imath] be correct if [imath]q(-1) \neq 0[/imath]?

 

[TheWrathOfMath]

How can your answer for [imath]q[/imath] be correct if [imath]q(-1) \neq 0[/imath]?

I believe that you copied 2cx+cx^2-2cx^3-cx^4 incorrectly.

It's not q(x) = 2x + x^2 - x^3 - x^4, but rather q(x) = 2x + x^2 - 2x^3 - x^4

 

[blamocur]

I was referring to your post # 21 :

c(2x+x^2-x^3-x^4), hence the basis for the intersection is {2x+x^2-x^3-x^4}.

 

[TheWrathOfMath]

I was referring to your post # 21 :

So apparently I miscopied it.
Thank you for pointing it out : )