1. The problem statement, all variables and given/known data[/b](adsbygoogle = window.adsbygoogle || []).push({});

Let V be the space of all polynomials of degree less than or equal to 2 over the reals. Define the transformation, H, as a mapping from V to R[x] by [tex](Hp)(x)=\int^x_{-1}p(t)dt\\[/tex]. a) Find the monic generator, d, which generates the ideal, M, containing the range of H.

b) If [tex]f\in{M\cap Range(H)[/tex] then [tex]f=dg[/tex] where d is given above. Show that [tex]g\in{V} [/tex].

2. Relevant equations

3. The attempt at a solution

I know the monic generator is the minimal polynomial which annihilates H. The way I would find the minimal polynomial is

1. find a basis for V

2. find the matrix representation for H with respect the basis

3. find the characteristic eqn of the matrix

4. the minimal polynomial divides the characteristic polynomial.

But when I try step 2, I keep getting a 4 x 3 matrix which doesn't have a determinant. So i don't know how I would find the characteristic eqn.

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# Homework Help: Monic Generator (Minimal Polynomial)

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