For each n, define two linear maps and X: Pn(R) Pn+1(R), (Xp)(x)= = xp(x), pe...

 

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For each n, define two linear maps and X: Pn(R) → Pn+1(R), (Xp)(x)= = xp(x), pe P₁ (R), x € R (Dp)(x) = p'(x), pe P₁ (R), z € R. D: Pn(R)→ Pn-1 (R), For n ≥ 1 compute the composition Do X: P₂ (R) → P₁ (R) and then: a) Compute the kernel of DoX b) Compute the image of Do X c) Determine if Do X is invertible d) Find the matrix of Do X with respect to the standard basis of P₁ (R), using the isomorphism P₁ (R) coming from the coordinate map e) What are the eigenvalues and eigenvectors of Do X? →R"+1 For each n, define two linear maps and X: Pn(R) → Pn+1(R), (Xp)(x)= = xp(x), pe P₁ (R), x € R (Dp)(x) = p'(x), pe P₁ (R), z € R. D: Pn(R)→ Pn-1 (R), For n ≥ 1 compute the composition Do X: P₂ (R) → P₁ (R) and then: a) Compute the kernel of DoX b) Compute the image of Do X c) Determine if Do X is invertible d) Find the matrix of Do X with respect to the standard basis of P₁ (R), using the isomorphism P₁ (R) coming from the coordinate map e) What are the eigenvalues and eigenvectors of Do X? →R"+1

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SOLUTION 633 M EIU Elv F W a W W 2 2 2 W 12a W 2 ... View the full answer