Please help me with part c We need the following definition for part (c) below. Vector spaces V and W are isomorphicif there is a linear transformation p: V → W that is a bijection, in the sense that(i) ø(u) = $(v)u = v for all u, v e V; and(ii) for all w E W there exists v e V such that o(v)= W.Consider the set P2 := {f: R → R : f(x) = ax² + bx + c for some a, b, c E R}. So P2 isthe set of polynomials of degree up to 2. This set is a vector space over R under additiongiven by(a1x2 + b1x + c1) + (a2x² + b2x + c2) = (a1 + a2)x² + (b1 + b2)x + (c1 + c2),and scalar multiplication given byX(ax? + bx + c) = Aax² + Abx + dc.Consider the function D: P2 –→ P2 given by D(ax² + bx + c) = 2ax + b.(a) Why did I call this function D?(b) Prove that D is a linear transformation'.(c) Find an n such that P2 is isomorphic to R". (Don't just state the value of n; provewhy the vector spaces are isomorphic.)(d) Let ø : P2 → R" be the function from (c) you used to show that P2 and R" areisomorphic (where n is your value from (c)). Find a matrix Ap such that po Doo-1is given by left multiplication by Ap.(e) Find the eigenvalues and eigenspaces of Ap.

Name: Please help me with part c We need the following definition for part (
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Please help me with part c We need the following definition for part (c) below. Vector spaces V and W are isomorphicif there is a linear transformation p: V → W that is a bijection, in the sense that(i) ø(u) = $(v)u = v for all u, v e V; and(ii) for