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Let D P3P3 be the function that sends a polynomial of degree 3 to its derivative (a) Find an eigenvector for D or explain why(b) Let B 1 x, x + x2, x2 + x3,x3}. B is a basis for P3. Find MDB-B Here, MD.- is the unique matrix such that MD-xs = [D(x)]sRecall that D: P is polynomial differentiation. 1x, x +x2, x2 +x3,x3} and C {1,x,x2,x3} be bases for P3 Let B (c) Express MDC

Let D P3P3 be the function that sends a polynomial of degree 3 to its derivative (a) Find an eigenvector for D or explain why no eigenvector exists Write your solution here
(b) Let B 1 x, x + x2, x2 + x3,x3}. B is a basis for P3. Find MDB-B Here, MD.- is the unique matrix such that MD-xs = [D(x)]s Write your solution here
Recall that D: P is polynomial differentiation. 1x, x +x2, x2 +x3,x3} and C {1,x,x2,x3} be bases for P3 Let B (c) Express MDCas a product of MD- matrices and appropriate change of coordinates Write your solution here
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Answer #1


(a) D(1) 0=0(1) 0 is eigen value and correcponds eigen vector is 1 D(x) 1k D(x2) 2x k D(x*) =3x2 there is no other eigen vect

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